Package 'FitVerse'

FitVerse: Parametric Distribution Fitting and Analysis

Description

FitVerse provides a unified, user-friendly interface for fitting parametric probability distributions to continuous univariate data. The package supports 52 distribution families spanning symmetric, right-skewed, heavy-tailed, bounded, and extreme-value shapes, and three estimation methods: Maximum Likelihood Estimation (MLE), Method of Moments (MOM), and L-Moments (LMOM).

Automatic best-fit selection is performed using AIC and BIC, supplemented by four goodness-of-fit tests: Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Cramer-von Mises (CvM), and Chi-Squared.

Every fitted model produces a publication-quality diagnostic plot: a histogram overlaid with the fitted density curve and the estimated PDF formula annotated directly on the figure. Additional diagnostic panels (Q-Q, P-P, CDF, Survival, Hazard, and Cumulative Hazard) are available via plot.fitverse().

FitVerse is designed as the data-characterisation layer of the OptiStrata ecosystem, with seamless handoff to stratifyR for optimal stratification of survey populations.

Main fitting functions

fitverse	Fit distributions to individual observations
fitverse_grouped	Fit distributions to grouped/interval data
fitverse_censored	Fit distributions to censored data
fitverse_batch	Fit all columns of a data frame
compare_dists	Return the ranked comparison table only
fitverse_distributions	List all 52 supported distributions

Probability tools

dfitverse	Density of the best-fit distribution
pfitverse	CDF of the best-fit distribution
qfitverse	Quantile function of the best-fit distribution
rfitverse	Random samples from the best-fit distribution
return_level	T-year return levels from the fitted model
lmrd	L-moment ratio diagram
ev_threshold	Extreme-value threshold stability plots

Inference and reporting

bootstrap_ci	Bootstrap confidence intervals for parameters
generate_report	Produce a self-contained HTML or PDF report
save_plot	Save the diagnostic plot to a file
to_json	Serialise a fitverse object to JSON

Sample datasets

FitVerse_datasets	Bundled CSV files for individual and grouped data
read_grouped_csv	Read a grouped-data CSV into list format

S3 methods for "fitverse" objects

print.fitverse	Concise best-fit summary
summary.fitverse	Full diagnostic report to the console
plot.fitverse	Diagnostic plots (density, Q-Q, P-P, CDF, etc.)
coef.fitverse	Extract parameter estimates
logLik.fitverse	Extract log-likelihood
AIC.fitverse	Extract AIC
BIC.fitverse	Extract BIC
as.list.fitverse	Convert to a serialisation-ready list

Supported distributions (52 families)

Shape	Distribution	Key
Symmetric	Normal	normal
Symmetric	Logistic	logistic
Symmetric	Cauchy	cauchy
Symmetric	Laplace	laplace
Symmetric	Student-t (location-scale)	student_t
Symmetric	Truncated Normal	truncnorm
Asymmetric	Skew-Normal	skewnormal
Asymmetric	Generalised Normal	gnorm
Asymmetric	Asymmetric Laplace	alaplace
Asymmetric	Johnson SU	johnsonsu
Right-skewed	Gamma	gamma
Right-skewed	Gamma (3-parameter)	gamma3
Right-skewed	Log-Normal	lognormal
Right-skewed	Log-Normal (3-parameter)	lognormal3
Right-skewed	Exponential	exponential
Right-skewed	Exponentiated Exponential	expexp
Right-skewed	Weibull (2-parameter)	weibull
Right-skewed	Weibull (3-parameter)	weibull3p
Right-skewed	Exponentiated Weibull	expweibull
Right-skewed	Log-Logistic	loglogistic
Right-skewed	Inverse Gaussian	invgaussian
Right-skewed	Inverse Gamma	invgamma
Right-skewed	Inverse Weibull	invweibull
Right-skewed	Gompertz	gompertz
Right-skewed	Birnbaum-Saunders	birnbaum_saunders
Right-skewed	Rayleigh	rayleigh
Right-skewed	Half-Normal	halfnormal
Right-skewed	Lindley	lindley
Right-skewed	Nakagami	nakagami
Heavy-tailed	Pareto	pareto
Heavy-tailed	Burr XII	burr
Heavy-tailed	Lomax (Pareto Type II)	lomax
Heavy-tailed	Paralogistic	paralogistic
Heavy-tailed	Dagum	dagum
Heavy-tailed	GB2 (Generalised Beta II)	gb2
Heavy-tailed	Normal Inverse Gaussian	nig
Heavy-tailed	Generalised Hyperbolic	ghyp
Heavy-tailed	Generalised Gamma	gengamma
Extreme value	Generalised Extreme Value	gev
Extreme value	Gumbel	gumbel
Extreme value	Generalised Pareto	gpd
Extreme value	Generalised Logistic	glo
Extreme value	Pearson Type III	pearson3
Extreme value	Log-Pearson Type III	lpearson3
Extreme value	Kappa-4	kap4
Extreme value	Wakeby	wakeby
Bounded	Beta	beta
Bounded	Uniform	uniform
Bounded	Triangular	triangular
Bounded	Right Triangular	rtriangle
Bounded	PERT	pert
Bounded	Kumaraswamy	kumaraswamy

Author(s)

Karuna G. Reddy [email protected] (University of Auckland, New Zealand)
M. G. M. Khan [email protected] (University of the South Pacific, Fiji)

Maintainer: Karuna G. Reddy [email protected]

References

Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society, Series B, 52(1), 105–124. doi:10.1111/j.2517-6161.1990.tb01775.x

Delignette-Muller, M. L. and Dutang, C. (2015). fitdistrplus: An R package for fitting distributions. Journal of Statistical Software, 64(4), 1–34. doi:10.18637/jss.v064.i04

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. doi:10.1109/TAC.1974.1100705

See Also

fitverse, fitverse_distributions, fitverse_grouped, FitVerse_datasets, fitdistrplus, actuar, lmomco

Examples

## Quick start: fit three distributions to simulated Gamma data
set.seed(42)
x <- rgamma(300, shape = 2, rate = 0.5)

fit <- fitverse(x,
                dists   = c("gamma", "lognormal", "weibull"),
                method  = "MLE",
                xlab    = "Waiting time (s)",
                plot    = FALSE,
                verbose = FALSE)

print(fit)

## See all 52 supported distributions
fitverse_distributions()

---

Bootstrap Confidence Intervals for Distribution Parameters

Description

Computes non-parametric percentile bootstrap confidence intervals for the parameters of the best-fit distribution in a fitverse object. Optionally also bootstraps confidence intervals for T-year return levels.

Usage

bootstrap_ci(fit,
             B              = 999L,
             conf           = 0.95,
             return_periods = NULL,
             progress       = NULL,
             seed           = NULL,
             verbose        = TRUE)

## S3 method for class 'fitverse_bootstrap'
print(x, ...)

Arguments

fit	An object of class "fitverse" as returned by fitverse(). The bootstrap uses the best-fit distribution and estimation method stored in fit$best_fit.
B	Integer: number of bootstrap replicates. Default 999. At least 199 is recommended; 1999 for publication-quality intervals.
conf	Numeric in $(0, 1)$: confidence level. Default 0.95 (95% CI).
return_periods	Numeric vector of return periods for which bootstrap CIs on return levels should be computed. NULL (default) skips this step. Example: return_periods = c(10, 50, 100).
progress	Optional function of the form function(p) where p is a numeric value in $[0, 1]$. Called after every 10% of replicates. Useful for shiny progress bars. Default NULL.
seed	Integer or NULL: random seed for reproducibility. Default NULL (no seed set).
verbose	Logical: print a progress message? Default TRUE.
x	An object of class "fitverse_bootstrap".
...	Currently unused.

Details

Algorithm

The non-parametric percentile bootstrap proceeds as follows:

1. Draw $B$ bootstrap samples of size $n$ with replacement from the observed data.

2. Re-fit the same distribution and estimation method to each sample, using the same internal engine as fitverse().

3. Collect the $B \times k$ matrix of parameter estimates (where $k$ is the number of parameters).

4. For each parameter, report the $\alpha/2$ and $1 - \alpha/2$ empirical percentiles of the bootstrap distribution as the lower and upper confidence bounds.

Replicates that fail to converge are excluded; a warning is issued if more than 10% fail.

Return-level CIs

When return_periods is supplied, the T-year return level is computed for each bootstrap replicate using return_level(), and the percentile CI is reported for each T.

Value

An S3 object of class "fitverse_bootstrap" with the following elements:

params_ci

Data frame with one row per parameter and columns: parameter, estimate, lower, upper, se_boot (bootstrap standard error).

return_level_ci

Data frame (or NULL if return_periods = NULL) with columns: T, return_level, lower, upper.

boot_params

Numeric matrix of dimension $B_{eff} \times k$: all successful bootstrap parameter estimates. Useful for plotting bootstrap distributions.

B

Integer: number of replicates requested.

B_eff

Integer: number of successful replicates.

conf

Numeric: confidence level.

dist_key

Character: distribution key.

method

Character: estimation method.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

References

Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.

Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge University Press.

See Also

return_level for point estimates without CIs.
fitverse for the initial fitting step.

Examples

set.seed(42)
x <- rgamma(200, shape = 2, rate = 0.5)
fit <- fitverse(x, dists = "gamma", plot = FALSE, verbose = FALSE)

boot <- bootstrap_ci(fit, B = 499, conf = 0.95, seed = 1, verbose = FALSE)
print(boot)

# Parameter CI data frame
boot$params_ci

# With return-level CIs
boot2 <- bootstrap_ci(fit, B = 499, return_periods = c(10, 50, 100),
                      seed = 1, verbose = FALSE)
boot2$return_level_ci

---

Compare Distribution Fits and Return a Ranking Table

Description

Fits one or more parametric distributions to a numeric vector and returns an ordered ranking table without producing a plot or a full fitverse object. Use this function when you want a quick tabular comparison and do not need the fitted-object infrastructure.

Usage

compare_dists(x,
              dists     = "all",
              method    = "MLE",
              criterion = "AIC",
              xlab      = "x",
              verbose   = TRUE)

Arguments

x	A numeric vector of observations. Non-finite values are removed automatically before fitting.
dists	Character vector of distribution keys, or "all" to try every compatible distribution. See fitverse_distributions().
method	Character vector: one or more of "MLE", "MOM", "LMOM". All results are combined into a single table when multiple methods are specified.
criterion	"AIC" (default) or "BIC": the criterion by which rows are sorted.
xlab	Character: a label for the data variable, passed through to any downstream functions. Default "x".
verbose	Logical: print progress messages? Default TRUE.

Details

compare_dists() calls the same internal fitting engine as fitverse() but skips GoF test computation, data-summary computation, and plotting. It is therefore faster and better suited to exploratory screening of many distributions or methods.

The returned data frame can be used directly with kable or datatable for reporting.

Value

A data frame with one row per distribution-method combination, ordered by the chosen information criterion (ascending), with columns:

Rank

Integer rank (1 = best).

Distribution

Full distribution name.

Method

Estimation method ("MLE", "MOM", or "LMOM").

N_params

Number of free parameters.

LogLik

Maximised log-likelihood.

AIC

Akaike Information Criterion.

Delta_AIC

AIC difference relative to the best model.

BIC

Bayesian Information Criterion.

Delta_BIC

BIC difference relative to the best model.

Converged

Logical: did the optimiser converge?

dist_key

Internal distribution key (character).

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

fitverse for a full fitted object plus diagnostic plot.

Examples

set.seed(1)
x <- rgamma(200, shape = 3, rate = 0.5)

tbl <- compare_dists(x,
                     dists   = c("gamma", "lognormal", "weibull", "exponential"),
                     method  = "MLE",
                     verbose = FALSE)
head(tbl)

---

Compute and Print a Descriptive Statistics Summary

Description

compute_data_summary() computes a comprehensive set of descriptive statistics for a numeric vector and returns them as a named list. print_data_summary() formats and prints that list to the console.

These functions are called automatically by fitverse() and summary.fitverse(), but can also be used independently for exploratory data analysis.

Usage

compute_data_summary(x, xlab = "x", n_raw = NULL)

print_data_summary(ds)

Arguments

x	A numeric vector, already cleaned of non-finite values (or not – the function removes them internally).
xlab	Character: variable name, stored in the returned list for labelling. Default "x".
n_raw	Integer or NULL: the original sample size before cleaning. If supplied, n_missing is computed as n_raw - n. If NULL, n_missing is set to NA.
ds	A named list as returned by compute_data_summary().

Details

Skewness and kurtosis are computed using the bias-corrected (unbiased) estimators:

$g_1 = \frac{n}{(n-1)(n-2)} \sum_{i=1}^n \left(\frac{x_i - \bar{x}}{s}\right)^3$

$g_2 = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum_{i=1}^n \left(\frac{x_i - \bar{x}}{s}\right)^4 - \frac{3(n-1)^2}{(n-2)(n-3)}$

These correspond to the skewness and kurtosis functions in the moments package (type 3 in e1071) and are consistent with the convention in Applied Statistics textbooks. The Normal distribution has skewness 0 and excess kurtosis 0.

Value

compute_data_summary() returns a named list with the following elements:

n

Integer: number of finite (non-missing) observations used.

n_missing

Integer or NA: number of non-finite values removed.

mean

Arithmetic mean.

sd

Standard deviation (denominator $n-1$).

cv

Coefficient of variation (sd / mean). NA when mean == 0.

median

Sample median.

iqr

Interquartile range ($Q_{0.75} - Q_{0.25}$).

skewness

Sample skewness (Fisher's $g_1$).

kurtosis

Excess kurtosis (Fisher's $g_2$).

min

Sample minimum.

max

Sample maximum.

range

Range (max - min).

q25

25th percentile.

q75

75th percentile.

xlab

Character: the variable label.

print_data_summary() invisibly returns ds.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

fitverse (calls this automatically), summary.fitverse.

Examples

set.seed(3)
x <- rlnorm(500, meanlog = 1, sdlog = 0.5)

ds <- compute_data_summary(x, xlab = "Claim amount", n_raw = 510)
print_data_summary(ds)

# Access individual statistics
ds$skewness
ds$cv

---

Density, CDF, Quantile, and Random Sampling for a Fitted Distribution

Description

Convenience functions that evaluate the probability density function (PDF), cumulative distribution function (CDF), quantile function (inverse CDF), and random-number generator for the best-fit distribution stored in a fitverse object.

These follow the standard R d/p/q/r naming convention and delegate to the underlying d*, p*, q*, and r* functions for the best-fit distribution.

Usage

dfitverse(x,   fit, log = FALSE)
pfitverse(q,   fit, lower.tail = TRUE, log.p = FALSE)
qfitverse(p,   fit, lower.tail = TRUE, log.p = FALSE)
rfitverse(n,   fit)

Arguments

x	Numeric vector of quantiles at which to evaluate the density.
q	Numeric vector of quantiles at which to evaluate the CDF.
p	Numeric vector of probabilities $p \in (0, 1)$.
n	Integer: number of random samples to generate.
fit	An object of class "fitverse" as returned by fitverse().
log, log.p	Logical: if TRUE, return (or accept) log-scale values. Default FALSE.
lower.tail	Logical: if TRUE (default), return $P(X \le q)$; if FALSE, return $P(X > q)$.

Details

The correct d/p/q/r functions are resolved via .lookup_dpqr(), which follows a two-step priority:

1. Internal closed-form implementations (highest priority): GEV, Gumbel, GPD, Pearson III, Log-Pearson III, and GLO all use FitVerse's own vectorised implementations registered in .FITVERSE_DPQR_OVERRIDES. This avoids any package-version signature issues with evd and provides full support for the new hydrological distributions that have no dedicated CRAN d/p/q/r package.

2. Package namespace lookup: For all other distributions, stats functions are found via match.fun(); Imports/Suggests packages (actuar, sn, mc2d) are resolved via getExportedValue().

The estimated parameters are extracted from fit$best_fit$params and passed as named arguments to the underlying function. This is equivalent to calling, for example, dgamma(x, shape = fit$best_fit$params["shape"], rate = fit$best_fit$params["rate"]).

Value

dfitverse()

Numeric vector of density values.

pfitverse()

Numeric vector of probabilities.

qfitverse()

Numeric vector of quantiles.

rfitverse()

Numeric vector of random samples.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

return_level for T-year return levels.
fitverse for the fitting step.

Examples

set.seed(42)
x <- rgamma(300, shape = 2, rate = 0.5)
fit <- fitverse(x, dists = "gamma", plot = FALSE, verbose = FALSE)

# Density at x = 2
dfitverse(2, fit)

# Probability that X <= 5
pfitverse(5, fit)

# 90th percentile
qfitverse(0.90, fit)

# Generate 10 random samples
rfitverse(10, fit)

---

Custom d/p/q/r Functions for Additional Distributions

Description

Density, CDF, quantile, and random-generation functions for distribution families that are either unavailable on CRAN, parameterised differently from existing packages, or implemented from scratch for performance and consistency within FitVerse.

The following families are covered:

Student-t (location-scale)

Three-parameter Student-t with location $\mu$, scale $\sigma > 0$, and degrees of freedom $\nu > 0$: dstudent_t, pstudent_t, qstudent_t, rstudent_t.

Laplace

Symmetric double-exponential with location $\mu$ and scale $b > 0$: dlaplace, plaplace, qlaplace, rlaplace.

Inverse Gaussian

Two-parameter (mean $\mu > 0$, shape $\lambda > 0$): dinvgaussian, pinvgaussian, qinvgaussian, rinvgaussian.

Lomax (Pareto Type II)

Shape $\alpha > 0$ and scale $\lambda > 0$: dlomax, plomax, qlomax, rlomax.

Generalised Gamma

Three-parameter generalisation of the Gamma (shape $p > 0$, scale $d > 0$, power $b > 0$): dgengamma, pgengamma, qgengamma, rgengamma.

Gompertz

Parameters $\alpha > 0$ and $\beta > 0$: dgompertz, pgompertz, qgompertz, rgompertz.

Birnbaum-Saunders (Fatigue-Life)

Shape $\alpha > 0$ and scale $\beta > 0$: dbirnbaum_saunders, pbirnbaum_saunders, qbirnbaum_saunders, rbirnbaum_saunders.

Rayleigh

Scale $\sigma > 0$: drayleigh, prayleigh, qrayleigh, rrayleigh.

Half-Normal

Scale $\sigma > 0$: dhalfnormal, phalfnormal, qhalfnormal, rhalfnormal.

Exponentiated Weibull

Shape parameters shape1 > 0 and shape2 > 0, scale scale > 0: dexpweibull, pexpweibull, qexpweibull, rexpweibull.

Three-Parameter Gamma

Gamma with location threshold $\gamma$ (shape $\alpha > 0$, scale $\beta > 0$, threshold $\gamma$): dgamma3, pgamma3, qgamma3, rgamma3.

Three-Parameter Log-Normal

Log-Normal with threshold $\gamma$ (meanlog $\mu$, sdlog $\sigma > 0$, threshold $\gamma$): dlnorm3, plnorm3, qlnorm3, rlnorm3.

Right Triangular

Special triangular with min and max, where the mode equals max: drtriangle, prtriangle, qrtriangle, rrtriangle.

Kumaraswamy

Bounded distribution with shape parameters shape1 > 0 and shape2 > 0 on $(0, 1)$: dkumaraswamy, pkumaraswamy, qkumaraswamy, rkumaraswamy.

Generalised Beta of the Second Kind (GB2)

Four-parameter family with shape1 > 0, scale > 0, shape2 > 0, shape3 > 0: dgb2, pgb2, qgb2, rgb2.

Kappa Four-Parameter

Generalised extreme-value family with location xi, scale alpha > 0, and shape parameters kappa and h: dkap4, pkap4, qkap4, rkap4.

Lindley

One-parameter distribution with theta > 0: dlindley, plindley, qlindley, rlindley.

Generalised Normal

Three-parameter distribution with location mu, scale sigma > 0, and shape beta > 0: dgnorm, pgnorm, qgnorm, rgnorm.

Dagum

Three-parameter Burr Type III with shape1 > 0, scale > 0, shape2 > 0: ddagum, pdagum, qdagum, rdagum.

Johnson SU

Four-parameter unbounded system with gamma, delta > 0, xi, lambda > 0: djohnsonsu, pjohnsonsu, qjohnsonsu, rjohnsonsu.

Asymmetric Laplace

Three-parameter asymmetric Laplace with location mu, scale sigma > 0, and asymmetry kappa > 0: dalaplace, palaplace, qalaplace, ralaplace.

Exponentiated Exponential

Two-parameter family with shape alpha > 0 and rate lambda > 0: dexpexp, pexpexp, qexpexp, rexpexp.

Normal-Inverse Gaussian (NIG)

Four-parameter family with location mu, spread delta > 0, steepness alpha > 0, and asymmetry beta: dnig, pnig, qnig, rnig.

Wakeby

Five-parameter quantile-defined distribution with location xi, scale parameters alpha and beta, and shape parameters gamma and delta: dwakeby, pwakeby, qwakeby, rwakeby.

Generalised Hyperbolic (GHyp)

Five-parameter family with lambda, alpha > 0, beta, delta > 0, mu: dghyp, pghyp, qghyp, rghyp.

Truncated Normal

Normal distribution truncated to $[a, b]$ with mean and sd > 0: dtruncnorm, ptruncnorm, qtruncnorm, rtruncnorm.

Nakagami

Two-parameter fading distribution with shape m >= 0.5 and spread Omega > 0: dnakagami, pnakagami, qnakagami, rnakagami.

Usage

dstudent_t(x,   nu, mu, sigma, log = FALSE)
pstudent_t(q,   nu, mu, sigma)
qstudent_t(p,   nu, mu, sigma)
rstudent_t(n,   nu, mu, sigma)

dlaplace(x,   mu, b, log = FALSE)
plaplace(q,   mu, b)
qlaplace(p,   mu, b)
rlaplace(n,   mu, b)

dinvgaussian(x,   mu, lambda, log = FALSE)
pinvgaussian(q,   mu, lambda)
qinvgaussian(p,   mu, lambda)
rinvgaussian(n,   mu, lambda)

dlomax(x,   alpha, lambda, log = FALSE)
plomax(q,   alpha, lambda)
qlomax(p,   alpha, lambda)
rlomax(n,   alpha, lambda)

dgengamma(x,   p, d, b, log = FALSE)
pgengamma(q,   p, d, b)
qgengamma(prob, p, d, b)
rgengamma(n,   p, d, b)

dgompertz(x,   alpha, beta, log = FALSE)
pgompertz(q,   alpha, beta)
qgompertz(p,   alpha, beta)
rgompertz(n,   alpha, beta)

dbirnbaum_saunders(x,   alpha, beta, log = FALSE)
pbirnbaum_saunders(q,   alpha, beta)
qbirnbaum_saunders(p,   alpha, beta)
rbirnbaum_saunders(n,   alpha, beta)

drayleigh(x,   sigma, log = FALSE)
prayleigh(q,   sigma, lower.tail = TRUE, log.p = FALSE)
qrayleigh(p,   sigma, lower.tail = TRUE, log.p = FALSE)
rrayleigh(n,   sigma)

dhalfnormal(x,   sigma, log = FALSE)
phalfnormal(q,   sigma, lower.tail = TRUE, log.p = FALSE)
qhalfnormal(p,   sigma, lower.tail = TRUE, log.p = FALSE)
rhalfnormal(n,   sigma)

dexpweibull(x,   shape1, scale, shape2, log = FALSE)
pexpweibull(q,   shape1, scale, shape2, lower.tail = TRUE, log.p = FALSE)
qexpweibull(p,   shape1, scale, shape2, lower.tail = TRUE, log.p = FALSE)
rexpweibull(n,   shape1, scale, shape2)

dgamma3(x,   shape, scale, thres, log = FALSE)
pgamma3(q,   shape, scale, thres, lower.tail = TRUE, log.p = FALSE)
qgamma3(p,   shape, scale, thres, lower.tail = TRUE, log.p = FALSE)
rgamma3(n,   shape, scale, thres)

dlnorm3(x,   meanlog, sdlog, thres, log = FALSE)
plnorm3(q,   meanlog, sdlog, thres, lower.tail = TRUE, log.p = FALSE)
qlnorm3(p,   meanlog, sdlog, thres, lower.tail = TRUE, log.p = FALSE)
rlnorm3(n,   meanlog, sdlog, thres)

drtriangle(x,   min, max, log = FALSE)
prtriangle(q,   min, max)
qrtriangle(p,   min, max)
rrtriangle(n,   min, max)

dkumaraswamy(x,   shape1, shape2, log = FALSE)
pkumaraswamy(q,   shape1, shape2)
qkumaraswamy(p,   shape1, shape2)
rkumaraswamy(n,   shape1, shape2)

dgb2(x, shape1, scale, shape2, shape3, log = FALSE)
pgb2(q, shape1, scale, shape2, shape3, lower.tail = TRUE, log.p = FALSE)
qgb2(p, shape1, scale, shape2, shape3, lower.tail = TRUE, log.p = FALSE)
rgb2(n, shape1, scale, shape2, shape3)

dkap4(x, xi, alpha, kappa, h, log = FALSE)
pkap4(q, xi, alpha, kappa, h, lower.tail = TRUE, log.p = FALSE)
qkap4(p, xi, alpha, kappa, h, lower.tail = TRUE, log.p = FALSE)
rkap4(n, xi, alpha, kappa, h)

dlindley(x, theta, log = FALSE)
plindley(q, theta, lower.tail = TRUE, log.p = FALSE)
qlindley(p, theta, lower.tail = TRUE, log.p = FALSE)
rlindley(n, theta)

dgnorm(x, mu, sigma, beta, log = FALSE)
pgnorm(q, mu, sigma, beta, lower.tail = TRUE, log.p = FALSE)
qgnorm(p, mu, sigma, beta, lower.tail = TRUE, log.p = FALSE)
rgnorm(n, mu, sigma, beta)

ddagum(x, shape1, scale, shape2, log = FALSE)
pdagum(q, shape1, scale, shape2, lower.tail = TRUE, log.p = FALSE)
qdagum(p, shape1, scale, shape2, lower.tail = TRUE, log.p = FALSE)
rdagum(n, shape1, scale, shape2)

djohnsonsu(x, gamma, delta, xi, lambda, log = FALSE)
pjohnsonsu(q, gamma, delta, xi, lambda, lower.tail = TRUE, log.p = FALSE)
qjohnsonsu(p, gamma, delta, xi, lambda, lower.tail = TRUE, log.p = FALSE)
rjohnsonsu(n, gamma, delta, xi, lambda)

dalaplace(x, mu, sigma, kappa, log = FALSE)
palaplace(q, mu, sigma, kappa, lower.tail = TRUE, log.p = FALSE)
qalaplace(p, mu, sigma, kappa, lower.tail = TRUE, log.p = FALSE)
ralaplace(n, mu, sigma, kappa)

dexpexp(x, alpha, lambda, log = FALSE)
pexpexp(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qexpexp(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rexpexp(n, alpha, lambda)

dnig(x, mu, delta, alpha, beta, log = FALSE)
pnig(q, mu, delta, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qnig(p, mu, delta, alpha, beta, lower.tail = TRUE, log.p = FALSE)
rnig(n, mu, delta, alpha, beta)

dwakeby(x, xi, alpha, beta, gamma, delta, log = FALSE)
pwakeby(q, xi, alpha, beta, gamma, delta, lower.tail = TRUE, log.p = FALSE)
qwakeby(p, xi, alpha, beta, gamma, delta, lower.tail = TRUE, log.p = FALSE)
rwakeby(n, xi, alpha, beta, gamma, delta)

dghyp(x, lambda, alpha, beta, delta, mu, log = FALSE)
pghyp(q, lambda, alpha, beta, delta, mu, lower.tail = TRUE, log.p = FALSE)
qghyp(p, lambda, alpha, beta, delta, mu, lower.tail = TRUE, log.p = FALSE)
rghyp(n, lambda, alpha, beta, delta, mu)

dtruncnorm(x, mean, sd, a, b, log = FALSE)
ptruncnorm(q, mean, sd, a, b, lower.tail = TRUE, log.p = FALSE)
qtruncnorm(p, mean, sd, a, b, lower.tail = TRUE, log.p = FALSE)
rtruncnorm(n, mean, sd, a, b)

dnakagami(x, m, Omega, log = FALSE)
pnakagami(q, m, Omega, lower.tail = TRUE, log.p = FALSE)
qnakagami(p, m, Omega, lower.tail = TRUE, log.p = FALSE)
rnakagami(n, m, Omega)

Arguments

x, q	Numeric vector of quantiles.
p	Numeric vector of probabilities in $(0, 1)$ for quantile functions; also the power shape parameter in dgengamma, pgengamma, qgengamma, and rgengamma.
prob	Numeric vector of probabilities in $(0, 1)$ for qgengamma (first argument, to avoid ambiguity with the p shape parameter).
n	Integer: number of observations to generate.
nu	Degrees of freedom for the Student-t ($\nu > 0$).
mu, sigma	Location and scale parameters.
b	Scale parameter for Laplace; also the shape parameter of the Generalised Gamma (used as the third shape in dgengamma etc.); also the upper truncation bound for dtruncnorm and related functions.
d	Depth shape parameter of the Generalised Gamma.
lambda	Inverse Gaussian shape parameter; Lomax scale parameter; Johnson SU scale parameter ($\lambda > 0$).
scale, shape	Scale and shape parameters.
shape1, shape2	Shape parameters.
alpha, beta	Gompertz and Birnbaum-Saunders parameters; Lomax uses alpha.
meanlog	Mean of the log-transformed variable (log-scale location) for dlnorm3/plnorm3/qlnorm3/rlnorm3.
sdlog	Standard deviation of the log-transformed variable (log-scale spread, $> 0$) for dlnorm3/plnorm3/qlnorm3/rlnorm3.
thres	Lower threshold (location shift) for 3-parameter distributions.
min, max	Support bounds for the Right Triangular.
log, log.p	Logical: if TRUE, probabilities are on the log scale.
lower.tail	Logical: if TRUE (default), $P(X \le q)$; otherwise $P(X > q)$.
shape3	Third shape parameter for dgb2 and related functions.
xi	Location parameter for Kappa, Wakeby, and Johnson SU distributions.
h	Lower shape parameter for the Kappa four-parameter distribution.
kappa	Upper shape parameter for the Kappa four-parameter distribution; also the asymmetry parameter for the Asymmetric Laplace.
theta	Rate parameter for the Lindley distribution ($\theta > 0$).
gamma	Shape parameter for the Johnson SU distribution; also a scale parameter in the Wakeby distribution.
delta	Shape parameter for the Johnson SU and Wakeby distributions; also the spread parameter for the NIG and GHyp distributions ($\delta > 0$).
m	Shape parameter for the Nakagami distribution ($m \ge 0.5$).
Omega	Spread parameter for the Nakagami distribution ($\Omega > 0$).
mean, sd	Mean and standard deviation for the Truncated Normal.
a	Lower truncation bound for dtruncnorm and related functions.

Value

A numeric vector of densities, probabilities, quantiles, or random samples, consistent with the standard R d/p/q/r convention.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

fitverse to fit these distributions to data; fitverse_distributions for the full distribution catalogue; dfitverse for evaluating the fitted best-fit distribution.

Examples

## Rayleigh
curve(drayleigh(x, sigma = 2), from = 0, to = 10,
      main = "Rayleigh(sigma=2)", ylab = "Density")

## Kumaraswamy (bounded to (0,1))
curve(dkumaraswamy(x, shape1 = 2, shape2 = 5), from = 0, to = 1,
      main = "Kumaraswamy(2, 5)", ylab = "Density")

## Birnbaum-Saunders round-trip
p <- c(0.1, 0.5, 0.9)
q <- qbirnbaum_saunders(p, alpha = 0.5, beta = 100)
pbirnbaum_saunders(q, alpha = 0.5, beta = 100)   # recovers p

## Inverse Gaussian random samples
set.seed(1)
x <- rinvgaussian(200, mu = 5, lambda = 10)
hist(x, breaks = 20, main = "Inverse Gaussian(5, 10)")

---

Three-Parameter Weibull Distribution

Description

Density, cumulative distribution function, quantile function, and random generation for the three-parameter Weibull distribution with shape $\beta > 0$, scale $\alpha > 0$, and threshold (location) $\gamma$. The support is $x > \gamma$.

Usage

dweibull3p(x,     shape, scale, thres, log = FALSE)
pweibull3p(q,     shape, scale, thres, lower.tail = TRUE, log.p = FALSE)
qweibull3p(p,     shape, scale, thres, lower.tail = TRUE, log.p = FALSE)
rweibull3p(n,     shape, scale, thres)

Arguments

x, q	Numeric vector of quantiles.
p	Numeric vector of probabilities in $(0, 1)$.
n	Integer: number of observations to generate.
shape	Positive shape parameter $\beta$.
scale	Positive scale parameter $\alpha$.
thres	Real-valued threshold (location) parameter $\gamma$. Values of x at or below thres have zero density.
log, log.p	Logical: if TRUE, return log-probabilities.
lower.tail	Logical: if TRUE (default), return $P(X \le q)$; otherwise $P(X > q)$.

Details

The three-parameter Weibull is a location-shifted version of the standard two-parameter Weibull. Let $Y = X - \gamma$; then $Y \sim \mathrm{Weibull}(\beta, \alpha)$. The PDF for $x > \gamma$ is

$f(x) = \frac{\beta}{\alpha} \left(\frac{x - \gamma}{\alpha}\right)^{\beta - 1} \exp\!\left[-\left(\frac{x - \gamma}{\alpha}\right)^{\beta}\right].$

Internally these functions shift x by thres and delegate to dweibull, pweibull, qweibull, and rweibull.

Value

dweibull3p

Numeric vector of density values.

pweibull3p

Numeric vector of probabilities.

qweibull3p

Numeric vector of quantiles.

rweibull3p

Numeric vector of random samples.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

dweibull for the two-parameter Weibull; fitverse with dists = "weibull3" to fit this distribution by MLE.

Examples

## PDF and CDF
curve(dweibull3p(x, shape = 2, scale = 10, thres = 5),
      from = 5, to = 35, ylab = "Density",
      main = "Weibull(2, 10) shifted by 5")

## Quantile / CDF round-trip
p  <- c(0.1, 0.5, 0.9)
q  <- qweibull3p(p, shape = 2, scale = 10, thres = 5)
pweibull3p(q, shape = 2, scale = 10, thres = 5)   # should recover p

## Random samples
set.seed(1)
x <- rweibull3p(200, shape = 1.8, scale = 50, thres = 10)
hist(x, breaks = 20, main = "Weibull(1.8, 50) with threshold 10")

---

Fit Probability Distributions to Univariate Continuous Data

Description

The primary function of the FitVerse package. Given a numeric data vector, fitverse() fits one or more parametric probability distributions, ranks them by an information criterion, selects the best-fitting model, computes goodness-of-fit statistics, and optionally produces a publication-quality diagnostic plot.

Three estimation methods are supported: Maximum Likelihood Estimation ("MLE"), Method of Moments ("MOM"), and L-Moments ("LMOM"). When multiple methods are requested, all results are combined into a single ranking table and the global best model is returned.

Tip: For a point-and-click experience, launch the built-in interactive Shiny application with FitVerseApp().

Usage

fitverse(x,
         dists       = "all",
         method      = "MLE",
         criterion   = "AIC",
         xlab        = "x",
         plot        = TRUE,
         interactive = FALSE,
         top_n       = 3L,
         progress    = NULL,
         verbose     = TRUE,
         ...)

Arguments

x	A numeric vector of observations. At least 4 finite values are required. Non-finite values (NA, NaN, Inf, -Inf) are removed automatically before fitting; a message is printed if any are found.
dists	Character vector of distribution keys to try, or "all" (default) to attempt every distribution whose support is compatible with the data. Use fitverse_distributions() to see all valid keys. Example: dists = c("gamma", "lognormal", "weibull").
method	Character vector specifying which estimation method(s) to use. One or more of: "MLE" Maximum Likelihood Estimation via numerical optimisation (fitdistrplus or custom stats::optim). Available for all 52 distributions. "MOM" Method of Moments. Uses closed-form expressions where available; numerical solution otherwise. Available for most of the 52 distributions. "LMOM" L-Moment estimation via lmomco. Available for distributions with L-moment parameter estimators. When multiple methods are supplied (e.g. method = c("MLE", "MOM")), all fits are combined and ranked together. Default: "MLE".
criterion	Character: the information criterion used for ranking and best-model selection. Either "AIC" (default) or "BIC". AIC is recommended for exploratory analysis and prediction; BIC imposes a stronger penalty for model complexity and is preferred when the goal is identifying the true generating distribution.
xlab	Character: a label for the data variable used in plot axis titles and the auto-generated report. Default "x". Example: xlab = "Annual maximum flood (m^3/s)".
plot	Logical: should a diagnostic plot be produced and printed? Default TRUE. Set to FALSE for batch workflows or when embedding in scripts. The plot can always be regenerated later with plot.fitverse().
interactive	Logical: if TRUE and the plotly package is installed, produces an interactive HTML figure instead of a static ggplot2 image. Default FALSE.
top_n	Integer: number of top-ranked distributions to overlay on the density panel of the diagnostic plot. The best-fit model is always drawn as a solid line; the remaining top_n - 1 are drawn as dashed lines. Default 3. Range: 1 to nrow(ranking).
progress	Optional function of the form function(p) where p is a numeric value in $[0, 1]$ indicating the proportion of work completed. Called at several points during fitting. Useful for updating a shiny progress bar. Default NULL (no callback). Example: progress = function(p) shiny::setProgress(p).
verbose	Logical: print progress messages to the console? Default TRUE. Set to FALSE in batch workflows or when running inside shiny.
...	Additional arguments passed to plot.fitverse().

Details

Workflow

fitverse() executes the following steps:

1. Validate and clean – removes non-finite values; checks that at least 4 observations remain.

2. Filter distributions – distributions whose support is incompatible with the data (e.g. positive-only Gamma when data contains negative values) are silently excluded.

3. Fit – calls fit_mle_all(), fit_mom_all(), and/or fit_lmom_all() according to method.

4. Goodness-of-fit – attaches Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and Cramer-von Mises (CvM) test results to each fit result.

5. Rank – builds a table ordered by criterion (ascending AIC or BIC).

6. Select – chooses the model with the lowest AIC (or BIC).

7. Summarise – computes compute_data_summary() and stores it in the returned object.

8. Plot (optional) – calls plot.fitverse().

Estimation methods

MLE

Maximises the log-likelihood $\ell(\boldsymbol\theta) = \sum_{i=1}^n \log f(x_i; \boldsymbol\theta)$. Implemented via fitdistrplus::fitdist() with bounded L-BFGS-B optimisation where parameter constraints exist.

MOM

Equates the first $k$ sample moments to their theoretical counterparts and solves for the $k$ parameters. Closed-form solutions are used where available (Normal, Gamma, Log-Normal, Exponential, Beta, Logistic, Uniform, Gumbel, Pareto, Inverse Gamma); numerical solution via stats::optimise() for Weibull and Log-Logistic. fitdistrplus MME is used for standard stats distributions.

LMOM

Equates sample L-moments (linear combinations of order statistics) to their theoretical counterparts. L-moments are more robust to outliers than conventional moments and are widely used in hydrology. Implemented via lmomco; available for Normal, Gamma, Exponential, Log-Normal, Weibull, GEV, GLO, Gumbel, Logistic, and Log-Logistic. Reference: Hosking (1990).

Model selection

The best-fit model is the one with the lowest AIC (or BIC) across all fitted distributions and methods. Delta AIC values in the ranking table quantify evidence against each model relative to the best: models with Delta AIC < 2 have "substantial support", 4–7 "considerably less", and > 10 "essentially none" (Burnham and Anderson, 2002).

Goodness-of-fit tests

Three non-parametric tests are applied to the best-fit model:

Kolmogorov-Smirnov (KS)

Measures the maximum absolute difference between the empirical and fitted CDFs. Conservative; not recommended as the primary criterion.

Anderson-Darling (AD)

Gives extra weight to the distribution tails. More powerful than KS for detecting tail departures. Implemented via goftest.

Cramer-von Mises (CvM)

Integrates the squared difference between empirical and fitted CDFs. Implemented via goftest.

A large p-value (> 0.05) indicates insufficient evidence to reject the fitted distribution.

Value

An S3 object of class "fitverse". It is a named list with the following elements:

best_fit

Named list describing the best-fitting model, with elements:

dist_key

Character: distribution key (e.g. "gamma").

method

Character: estimation method ("MLE", "MOM", or "LMOM").

params

Named numeric vector of parameter estimates.

loglik

Numeric: maximised log-likelihood.

aic

Numeric: Akaike Information Criterion.

bic

Numeric: Bayesian Information Criterion.

n_params

Integer: number of estimated parameters.

n

Integer: sample size used.

converged

Logical: did the optimiser converge?

gof

Data frame of goodness-of-fit test results (Test, Statistic, P_value, Stars), or NULL if unavailable.

all_fits

Named list of all fit-result lists, one per distribution-method combination. Keys are of the form "distkey_METHOD" (e.g. "gamma_MLE").

ranking

Data frame with columns: Rank, Distribution, Method, N_params, LogLik, AIC, Delta_AIC, BIC, Delta_BIC, KS_p, AD_p, Converged, dist_key. Ordered by the chosen criterion (ascending).

data

Numeric vector: the cleaned input data.

n

Integer: number of finite observations used.

xlab

Character: the variable label.

data_summary

Named list from compute_data_summary(): n, n_missing, mean, sd, cv, median, iqr, skewness, kurtosis, min, max, range, q25, q75.

criterion

Character: "AIC" or "BIC".

method

Character vector: method(s) used.

call

The matched function call.

The object is returned invisibly. Use print(), summary(), plot(), coef(), logLik(), AIC(), and BIC() for standard S3 method access.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

References

Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference (2nd ed.). Springer.

Delignette-Muller, M. L. and Dutang, C. (2015). fitdistrplus: An R package for fitting distributions. Journal of Statistical Software, 64(4), 1–34. doi:10.18637/jss.v064.i04

Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society, Series B, 52(1), 105–124.

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.

See Also

compare_dists for a ranking table only (no plot).
fitverse_distributions to list all supported distributions.
plot.fitverse, summary.fitverse, bootstrap_ci, return_level, generate_report.

Examples

## -----------------------------------------------------------
## Example 1: Basic MLE fit -- three distributions
## -----------------------------------------------------------
set.seed(42)
x <- rgamma(300, shape = 2, rate = 0.5)

fit <- fitverse(x,
                dists   = c("gamma", "lognormal", "weibull"),
                method  = "MLE",
                xlab    = "Waiting time (s)",
                plot    = FALSE,
                verbose = FALSE)

print(fit)
coef(fit)        # parameter estimates
AIC(fit)         # AIC of the best-fit model
logLik(fit)      # log-likelihood

## -----------------------------------------------------------
## Example 2: All three estimation methods, ranked by BIC
## -----------------------------------------------------------

fit2 <- fitverse(x,
                 method    = c("MLE", "MOM", "LMOM"),
                 criterion = "BIC",
                 plot      = FALSE,
                 verbose   = FALSE)
summary(fit2)


## -----------------------------------------------------------
## Example 3: Automatic best-fit selection across all distributions
## -----------------------------------------------------------

set.seed(7)
x3 <- rlnorm(500, meanlog = 1.5, sdlog = 0.6)

fit3 <- fitverse(x3,
                 xlab    = "Insurance claim size",
                 method  = "MLE",
                 plot    = FALSE,
                 verbose = FALSE)
fit3$ranking[1:5, c("Distribution","Method","AIC","Delta_AIC","AD_p")]


## -----------------------------------------------------------
## Example 4: Accessing the data summary
## -----------------------------------------------------------

fit4 <- fitverse(x, plot = FALSE, verbose = FALSE)
fit4$data_summary$mean
fit4$data_summary$skewness

---

Fit Distributions to All Columns of a Data Frame

Description

Applies fitverse() to every numeric column of a data frame (or matrix, or named list), collects the results, and returns a tidy summary table alongside the full list of fitted objects.

Use fitverse_batch() for automated data characterisation workflows, survey-population profiling, or as a pre-processing step before optimal stratification with stratifyR.

Usage

fitverse_batch(data,
               cols      = NULL,
               dists     = "all",
               method    = "MLE",
               criterion = "AIC",
               top_n     = 3L,
               plot      = FALSE,
               progress  = NULL,
               verbose   = TRUE)

## S3 method for class 'fitverse_batch'
print(x, ...)

## S3 method for class 'fitverse_batch'
summary(object, ...)

Arguments

data	A data.frame, matrix, or named list of numeric vectors. Non-numeric columns are silently ignored.
cols	Character vector of column names to process. If NULL (default), all numeric columns are processed.
dists	Distribution keys to try, or "all". Passed to fitverse().
method	Estimation method(s): "MLE", "MOM", "LMOM", or a character vector of multiple methods. Default "MLE".
criterion	"AIC" or "BIC". Default "AIC".
top_n	Integer: number of top-ranked distributions stored in each fit. Default 3.
plot	Logical: produce and print a diagnostic plot for each variable? Default FALSE (recommended for batch use).
progress	Optional callback function(p) for reporting overall batch progress, where p is a value in $[0, 1]$.
verbose	Logical: print per-column progress messages? Default TRUE.
x, object	An object of class "fitverse_batch".
...	Currently unused.

Details

fitverse_batch() iterates over columns with a tryCatch() wrapper so that a fitting failure for one column does not abort the entire batch. Failed columns are collected in the failed element of the returned object.

Column names containing spaces or special characters are handled correctly via make.names() internally.

Value

An S3 object of class "fitverse_batch" with elements:

fits

Named list of "fitverse" objects, one per successfully fitted column.

summary

Data frame with one row per column, columns: variable, n, best_dist, method, AIC, BIC, loglik, KS_p, AD_p.

failed

Character vector of column names for which fitting failed, or character(0) if all succeeded.

criterion

Character: the criterion used.

call

The matched call.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

fitverse for single-column fitting.
generate_report for producing a report from batch results.

Examples

# Fit all numeric columns of the airquality dataset
data(airquality)
batch <- fitverse_batch(airquality,
                        method  = "MLE",
                        verbose = FALSE)
print(batch)
summary(batch)

# Access the fit for the Ozone column
batch$fits[["Ozone"]]

---

Fit Parametric Distributions to Censored or Truncated Data

Description

Estimates distribution parameters by maximising the censored log-likelihood for data that may be right-censored, left-censored, interval-censored, and/or left-/right-truncated, or any combination of these. Seven distribution families are supported. Fits are ranked by AIC or BIC, and a nonparametric Kaplan–Meier estimate is overlaid automatically on the survival or CDF plot.

Usage

fitverse_censored(x,
                  status      = NULL,
                  x_upper     = NULL,
                  trunc_lower = -Inf,
                  trunc_upper =  Inf,
                  dists       = c("normal", "lognormal", "weibull",
                                  "exponential", "gamma",
                                  "loglogistic", "gumbel"),
                  criterion   = c("AIC", "BIC"),
                  n_starts    = 3L,
                  xlab        = "x",
                  draw        = TRUE)

## S3 method for class 'fitverse_censored'
print(x, ...)

## S3 method for class 'fitverse_censored'
plot(x, top_n = 3L, ...)

Arguments

x	Numeric vector of observed or censored values. For right-censored observations this is the last observed time; for left-censored observations it is the detection-limit value; for interval-censored observations it is the lower bound of the interval. In print and plot methods, x is the "fitverse_censored" object.
status	Integer vector of the same length as x encoding the observation type using the survival-package convention: 1 Completely observed (event occurred). 0 Right-censored (event had not yet occurred at last follow-up). 2 Left-censored (true value is below a detection limit). 3 Interval-censored (true value lies in [x, x_upper]). If NULL (default), all observations are treated as completely observed (status = 1).
x_upper	Numeric vector of upper bounds for interval-censored observations (status == 3). Must be the same length as x. Ignored for all rows where status != 3.
trunc_lower	Numeric scalar: left (lower) truncation bound. Observations below this value are never recorded; the likelihood is normalised by $P(X > \texttt{trunc\_lower})$. Default -Inf (no left truncation).
trunc_upper	Numeric scalar: right (upper) truncation bound. Default Inf (no right truncation).
dists	Character vector of distribution keys to fit. Any subset of c("normal", "lognormal", "weibull", "exponential", "gamma", "loglogistic", "gumbel"). Default: all seven.
criterion	Character: "AIC" (default) or "BIC". Used to rank the fitted distributions.
n_starts	Positive integer: number of random starting points per distribution. Increasing this reduces the risk of the optimiser converging to a local optimum. Default 3.
xlab	Character: variable label used in plot axis titles. Default "x".
draw	Logical: produce a survival-function (right-censored) or cumulative-distribution (otherwise) plot? Default TRUE.
top_n	Positive integer: number of top-ranked distributions to overlay on the plot. Default 3.
...	Further arguments passed to or from other methods.

Value

An object of class "fitverse_censored", which is a named list with the following elements:

fits

List of fit objects ordered by criterion (best first). Each element is a list with: dist_key (character), display (character display name), par (named numeric vector of parameter estimates), log_lik (numeric), aic (numeric), bic (numeric), n_par (integer), converged (logical).

rankings

Data frame with columns Rank, Distribution, LogLik, AIC, BIC, Converged, sorted by criterion.

x, status, x_upper

Cleaned copies of the input data vectors (non-finite values removed).

trunc_lower, trunc_upper

Truncation bounds as supplied.

xlab

Variable label.

criterion

Ranking criterion used ("AIC" or "BIC").

References

Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data. Wiley, New York.

Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data, 2nd ed. Wiley, Hoboken.

Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481. doi:10.1080/01621459.1958.10501452

See Also

fitverse for uncensored data fitting; fitverse_distributions for the full distribution library.

Examples

## Right-censored survival data (Weibull true model)
set.seed(1)
times  <- rweibull(100, shape = 1.8, scale = 50)
censor <- rexp(100, rate = 1/60)
x      <- pmin(times, censor)
status <- as.integer(times <= censor)   # 1 = event, 0 = right-censored

fit_s <- fitverse_censored(x, status,
                           dists = c("weibull", "lognormal", "gamma"),
                           xlab  = "Survival time (hours)")
print(fit_s)
plot(fit_s, top_n = 3)


## Left-censored environmental data (below detection limit)
set.seed(2)
conc       <- rlnorm(80, meanlog = 1.5, sdlog = 0.7)
dl         <- 3.0
x_env      <- ifelse(conc >= dl, conc, dl)
status_env <- ifelse(conc >= dl, 1L, 2L)

fit_e <- fitverse_censored(x_env, status_env,
                           dists = c("lognormal", "gamma"),
                           xlab  = "Concentration (mg/L)")
fit_e$rankings


## Left-truncated occupational exposure data
set.seed(3)
exposure <- rlnorm(300, meanlog = 2.5, sdlog = 0.5)
exposure <- exposure[exposure > 5]   # only workers above LOQ recorded

fit_t <- fitverse_censored(exposure, trunc_lower = 5,
                           dists = c("lognormal", "gamma", "weibull"),
                           xlab  = "Exposure (mg/m3)")
fit_t$fits[[1L]]$par

---

Sample Datasets Bundled with FitVerse

Description

FitVerse includes several comma-separated value (CSV) files in inst/extdata/ that can be used to explore the package's fitting functions. All files are accessed with system.file().

Individual-observation datasets (for fitverse())

annual_max_flows.csv

Annual maximum daily peak flows (m$^3$/s) for the Rewa River at Navolau, Fiji, covering a 75-year record (1950–2024). The data are right-skewed; Gumbel, GEV, Log-Pearson III, and Log-Normal are natural candidates.

wind_speeds.csv

Daily maximum wind gust speeds (m/s) recorded at Nadi Airport, Fiji, over 200 days (2020–2024). Weibull and Rayleigh distributions are commonly used for wind data.

failure_times.csv

Failure times (hours) from a life test of 150 aluminium electrolytic capacitors under 85 ${}^\circ$C stress. Weibull, Gamma, Log-Normal, and Birnbaum-Saunders are typical reliability choices.

insurance_claims.csv

Residential property insurance claim amounts (in thousands of USD) from 180 claims settled by Pacific Insurance Ltd between 2018 and 2024. Log-Normal, Gamma, and Pareto distributions are common in loss modelling.

concrete.csv

Compressive strength (MPa) and mix-design variables for 1030 concrete specimens (UCI Machine Learning Repository). The Strength column is suitable for fitting; Normal, Gamma, and Weibull are plausible choices.

Grouped / interval-censored datasets (for fitverse_grouped())

rainfall_grouped.csv

Annual maximum daily rainfall (mm) at Suva, Fiji, summarised into a frequency table with columns midpoint and count (80 years of record).

failure_times_grouped.csv

Failure times for 120 electronic components given as an interval frequency table with columns lower, upper, and count.

insurance_losses_grouped.csv

Property insurance claim amounts for 250 claims given as an interval frequency table with columns lower, upper, and count.

Format

Each file is a plain-text CSV with a column-name header row. Lines beginning with # are comments describing the dataset. All numeric values use the standard decimal point.

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

fitverse for fitting to individual observations.
fitverse_grouped for fitting to grouped / interval data.

Examples

## Annual maximum flows
path <- system.file("extdata", "annual_max_flows.csv", package = "FitVerse")
x <- read.csv(path, comment.char = "#")$peak_flow_m3s
summary(x)


fit <- fitverse(x, xlab = "Peak flow (m3/s)", plot = FALSE)
print(fit)


## Grouped rainfall data
gpath <- system.file("extdata", "rainfall_grouped.csv", package = "FitVerse")
dat   <- read_grouped_csv(gpath)

gfit  <- fitverse_grouped(midpoints = dat$midpoints, counts = dat$counts,
                          xlab = "Rainfall (mm)")
print(gfit)

---

List All Distributions Supported by FitVerse

Description

Returns a data frame describing all 52 probability distributions that FitVerse can fit, including their distribution keys, full names, number of parameters, support, available estimation methods, and the underlying R function source.

This page also documents the mathematical details of the four hydrological / extreme-value distributions: Generalised Pareto (GPD), Pearson Type III (P3), Log-Pearson Type III (LP3), and Generalised Logistic (GLO).

Usage

fitverse_distributions(method = NULL)

Arguments

method

Optional character scalar: filter to distributions available for a specific estimation method. One of "MLE", "MOM", or "LMOM". If NULL (default), all 52 distributions are returned.

Details

Complete distribution table (52 families)

Key	Distribution	Params	Support	Family
normal	Normal	2	$(-\infty,\infty)$	Symmetric
logistic	Logistic	2	$(-\infty,\infty)$	Symmetric
cauchy	Cauchy	2	$(-\infty,\infty)$	Symmetric
laplace	Laplace	2	$(-\infty,\infty)$	Symmetric
student_t	Student-t (location-scale)	3	$(-\infty,\infty)$	Symmetric
truncnorm	Truncated Normal	4	$[a,b]$	Symmetric
skewnormal	Skew-Normal	3	$(-\infty,\infty)$	Asymmetric
gnorm	Generalised Normal	3	$(-\infty,\infty)$	Asymmetric
alaplace	Asymmetric Laplace	3	$(-\infty,\infty)$	Asymmetric
johnsonsu	Johnson SU	4	$(-\infty,\infty)$	Asymmetric
gamma	Gamma	2	$(0,\infty)$	Right-skewed
gamma3	Gamma (3-parameter)	3	$(\mu,\infty)$	Right-skewed
lognormal	Log-Normal	2	$(0,\infty)$	Right-skewed
lnorm3	Log-Normal (3-parameter)	3	$(\mu,\infty)$	Right-skewed
exponential	Exponential	1	$(0,\infty)$	Right-skewed
expexp	Exponentiated Exponential	2	$(0,\infty)$	Right-skewed
weibull	Weibull (2-parameter)	2	$(0,\infty)$	Right-skewed
weibull3p	Weibull (3-parameter)	3	$(\mu,\infty)$	Right-skewed
expweibull	Exponentiated Weibull	3	$(0,\infty)$	Right-skewed
loglogistic	Log-Logistic	2	$(0,\infty)$	Right-skewed
invgaussian	Inverse Gaussian	2	$(0,\infty)$	Right-skewed
invgamma	Inverse Gamma	2	$(0,\infty)$	Right-skewed
invweibull	Inverse Weibull	2	$(0,\infty)$	Right-skewed
gompertz	Gompertz	2	$(0,\infty)$	Right-skewed
birnbaum_saunders	Birnbaum-Saunders	2	$(0,\infty)$	Right-skewed
rayleigh	Rayleigh	1	$(0,\infty)$	Right-skewed
halfnormal	Half-Normal	1	$(0,\infty)$	Right-skewed
lindley	Lindley	1	$(0,\infty)$	Right-skewed
nakagami	Nakagami	2	$(0,\infty)$	Right-skewed
gengamma	Generalised Gamma	3	$(0,\infty)$	Right-skewed
pareto	Pareto	2	$(x_m,\infty)$	Heavy-tailed
burr	Burr XII	3	$(0,\infty)$	Heavy-tailed
lomax	Lomax (Pareto Type II)	2	$(0,\infty)$	Heavy-tailed
paralogistic	Paralogistic	2	$(0,\infty)$	Heavy-tailed
dagum	Dagum	3	$(0,\infty)$	Heavy-tailed
gb2	GB2 (Generalised Beta II)	4	$(0,\infty)$	Heavy-tailed
nig	Normal Inverse Gaussian	4	$(-\infty,\infty)$	Heavy-tailed
ghyp	Generalised Hyperbolic	5	$(-\infty,\infty)$	Heavy-tailed
gev	Generalised Extreme Value	3	depends on shape	Extreme-value
gumbel	Gumbel (Type I EV)	2	$(-\infty,\infty)$	Extreme-value
gpd	Generalised Pareto	3	$[\mu,\infty)$ or bdd	Extreme-value
glo	Generalised Logistic	3	depends on shape	Extreme-value
pearson3	Pearson Type III	3	$(-\infty,\infty)$	Extreme-value
lpearson3	Log-Pearson Type III	3	$(0,\infty)$	Extreme-value
kap4	Kappa-4	4	depends on shape	Extreme-value
wakeby	Wakeby	5	$(0,\infty)$	Extreme-value
beta	Beta	2	$(0,1)$	Bounded
uniform	Uniform	2	$[a,b]$	Bounded
triangular	Triangular	3	$[a,b]$	Bounded
rtriangle	Right Triangular	2	$[a,b]$	Bounded
pert	PERT (Beta-PERT)	3	$[a,b]$	Bounded
kumaraswamy	Kumaraswamy	2	$(0,1)$	Bounded

Hydrological and extreme-value distributions (v1.0 additions)

The four distributions below – GPD, Pearson III, Log-Pearson III, and GLO – are central to flood-frequency analysis and Peaks-Over-Threshold modelling. They share a common implementation strategy: closed-form d/p/q/r functions are registered in the internal .FITVERSE_DPQR_OVERRIDES table, bypassing any external package dependency and guaranteeing consistent behaviour across platforms.

Generalised Pareto Distribution (GPD) – key: "gpd"

Parameters: $\mu$ (location / threshold), $\sigma > 0$ (scale), $\xi$ (shape).

PDF ($\xi \neq 0$):

$f(x\,;\,\mu,\sigma,\xi)=\frac{1}{\sigma} \Bigl(1+\xi\,\frac{x-\mu}{\sigma}\Bigr)^{-1/\xi-1}$

Support: $x \ge \mu$ when $\xi \ge 0$; $\mu \le x \le \mu - \sigma/\xi$ when $\xi < 0$. Reduces to $\mathrm{Exp}(1/\sigma)$ when $\xi = 0$.

Quantile function:

$Q(p)=\mu+\frac{\sigma}{\xi}\bigl[(1-p)^{-\xi}-1\bigr],\quad\xi\neq 0 \qquad Q(p)=\mu-\sigma\log(1-p),\quad\xi=0$

Method of Moments: Fix $\hat\mu=\min(x)-\varepsilon$; let $y_i=x_i-\hat\mu$. Then $\hat\xi=(1-\bar y^2/s_y^2)/2$, $\hat\sigma=\bar y(1-\hat\xi)$. Valid only when $\hat\xi<1/2$.

L-Moments: via lmomco::pargpa(). Sign convention: FitVerse $\xi=-\kappa_{\text{lmomco}}$.

Use case: Peaks-Over-Threshold analysis; insurance excess-of-loss modelling (Pickands, 1975).

Pearson Type III (P3) – key: "pearson3"

Parameters: $\alpha>0$ (shape), $\beta$ (scale; may be negative), $\zeta$ (location).

Relationship to Gamma:

$X\sim\mathrm{P3}(\alpha,\beta,\zeta) \;\Leftrightarrow\; (X-\zeta)/\beta\sim\mathrm{Gamma}(\alpha,\,\mathrm{rate}=1)$

PDF:

$f(x\,;\,\alpha,\beta,\zeta)= \frac{|\beta|^{-1}}{\Gamma(\alpha)} \Bigl(\frac{x-\zeta}{\beta}\Bigr)^{\!\alpha-1} \exp\!\Bigl(-\frac{x-\zeta}{\beta}\Bigr), \quad\frac{x-\zeta}{\beta}>0$

Positive $\beta$ gives right-skewed; negative $\beta$ gives left-skewed data.

Method of Moments: Let $\bar x,s,g$ be the sample mean, standard deviation, and skewness coefficient. Then:

$\hat\alpha=4/g^2,\qquad\hat\beta=sg/2,\qquad\hat\zeta=\bar x-2s/g$

L-Moments: via lmomco::parpe3(), which returns $(\mu,\sigma,\gamma)$. FitVerse converts using the MOM formulae above.

Use case: Annual peak-flow frequency analysis (US Bulletin 17C; England et al., 2019); meteorological extremes.

Log-Pearson Type III (LP3) – key: "lpearson3"

Parameters: $\alpha>0$ (shape), $\beta$ (scale), $\zeta$ (location) – all defined in log-space.

$X\sim\mathrm{LP3}(\alpha,\beta,\zeta) \;\Leftrightarrow\; \log X\sim\mathrm{P3}(\alpha,\beta,\zeta)$

PDF:

$f(x\,;\,\alpha,\beta,\zeta) =\frac{f_{\mathrm{P3}}(\log x\,;\,\alpha,\beta,\zeta)}{x},\quad x>0$

CDF and quantile:

$F(x)=F_{\mathrm{P3}}(\log x),\qquad Q(p)=\exp\bigl[Q_{\mathrm{P3}}(p)\bigr]$

Method of Moments and L-Moments: Pearson III estimators applied to $\log x_i$. L-Moments use lmomco::parpe3() on the log-transformed sample.

Use case: The US federal standard for flood-frequency estimation (Bulletin 17C; England et al., 2019).

Generalised Logistic Distribution (GLO) – key: "glo"

Parameters: $\xi$ (location), $\alpha>0$ (scale), $\kappa$ (shape).

CDF ($\kappa\neq 0$):

$F(x\,;\,\xi,\alpha,\kappa) =\frac{1}{1+\bigl[1-\kappa(x-\xi)/\alpha\bigr]^{1/\kappa}}$

Reduces to $\mathrm{Logistic}(\xi,\alpha)$ when $\kappa=0$.

Quantile function:

$Q(p)=\xi+\frac{\alpha}{\kappa}\Bigl[1-\Bigl(\frac{1-p}{p}\Bigr)^{\!\kappa}\Bigr], \quad\kappa\neq 0 \qquad Q(p)=\xi+\alpha\log\frac{p}{1-p},\quad\kappa=0$

Support: $(-\infty,\,\xi+\alpha/\kappa)$ for $\kappa>0$; $(\xi+\alpha/\kappa,\,\infty)$ for $\kappa<0$; all real for $\kappa=0$.

L-Moments: via lmomco::parglo(). No sign flip: FitVerse $\kappa=\kappa_{\text{lmomco}}$.

MOM is not implemented for GLO (complex moment system; use LMOM or MLE).

Use case: The recommended flood-frequency distribution in the United Kingdom (WINFAP; Robson & Reed, 1999).

L-moment shape-parameter sign conventions

lmomco uses the opposite sign for the shape parameter of GEV and GPD:

Distribution	lmomco $\kappa$	FitVerse shape
GEV	$\kappa$	$-\kappa$ (sign flip)
GPD	$\kappa$	$-\kappa$ (sign flip)
GLO	$\kappa$	$\kappa$ (no flip)

Value

A data frame with one row per distribution and columns:

Key

Character: the string to pass in the dists argument of fitverse() and related functions.

Name

Full distribution name.

Family

Broad family tag (e.g. "Extreme-value", "Right-skewed").

Package

The R package supplying d/p/q/r functions, or NA for distributions with FitVerse-internal implementations.

MLE

Character "Yes" or "-": MLE available?

MOM

Character "Yes" or "-": MOM available?

LMOM

Character "Yes" or "-": L-Moments available?

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

References

England, J. F., Jr., et al. (2019). Guidelines for Determining Flood Flow Frequency – Bulletin 17C. USGS Techniques and Methods, Book 4, Chapter B5.

Hosking, J. R. M. and Wallis, J. R. (1997). Regional Frequency Analysis: An Approach Based on L-moments. Cambridge University Press.

Pickands, J. (1975). Statistical inference using extreme order statistics. The Annals of Statistics, 3(1), 119–131.

Robson, A. and Reed, D. (1999). Flood Estimation Handbook, Volume 3. Institute of Hydrology, Wallingford, UK.

See Also

fitverse for fitting any of the 52 distributions.
compare_dists for quick multi-distribution screening.
return_level for T-year return levels.
bootstrap_ci for parametric bootstrap confidence intervals.

Examples

# All 52 distributions
fitverse_distributions()

# Only those with L-moment support
fitverse_distributions(method = "LMOM")

# Extreme-value / hydrological families
ev <- fitverse_distributions()
ev[ev$Key %in% c("gev","gumbel","gpd","pearson3","lpearson3","glo"), ]

## ---- GPD (Peaks-Over-Threshold) ----------------------------------------
set.seed(42)
x_excess <- evd::rgpd(300, loc = 0, scale = 2, shape = 0.1)
fit_gpd   <- fitverse(x_excess, dists = "gpd", method = "LMOM",
                      plot = FALSE, verbose = FALSE)
coef(fit_gpd)
return_level(fit_gpd, return_periods = c(10, 50, 100))

## ---- Pearson III (Bulletin 17C style) ----------------------------------
## Pearson III with shape=5, scale=3, loc=10 is equivalent to
## a shifted Gamma: X = loc + Gamma(shape, scale)
set.seed(42)
x_p3  <- rgamma(200, shape = 5, scale = 3) + 10
fit_p3 <- fitverse(x_p3, dists = "pearson3", method = "LMOM",
                   plot = FALSE, verbose = FALSE)
coef(fit_p3)

## ---- Log-Pearson III ----------------------------------------------------
## Log-Pearson III: log(X) ~ Pearson III(shape, scale, loc)
## so X = exp(loc + Gamma(shape, scale))
set.seed(42)
x_lp3  <- exp(rgamma(200, shape = 5, scale = 0.4) + 2)
fit_lp3 <- fitverse(x_lp3, dists = "lpearson3", method = "LMOM",
                    plot = FALSE, verbose = FALSE)
coef(fit_lp3)

## ---- GLO (UK WINFAP style) ----------------------------------------------
## Generate GLO samples via the lmomco quantile function
set.seed(42)
x_glo  <- lmomco::qlmomco(runif(200),
             lmomco::vec2par(c(50, 8, 0.12), type = "glo"))
fit_glo <- fitverse(x_glo, dists = "glo", method = "LMOM",
                    plot = FALSE, verbose = FALSE)
coef(fit_glo)
return_level(fit_glo, return_periods = c(2, 10, 50, 100, 200))

---

Fit Distributions to Grouped or Interval-Censored Data

Description

fitverse_grouped() fits one or more parametric distributions to data that are available only in grouped (frequency-table) or interval-censored form. It accepts either class midpoints with counts, or explicit lower and upper interval boundaries with counts.

read_grouped_csv() reads a two- or three-column CSV file into the format expected by fitverse_grouped().

Usage

fitverse_grouped(midpoints = NULL,
                 counts,
                 lower   = NULL,
                 upper   = NULL,
                 dists   = "auto",
                 method  = "All",
                 xlab    = "x",
                 top_n   = 5L,
                 verbose = FALSE)

read_grouped_csv(file, sep = ",")

Arguments

midpoints	Numeric vector of class midpoints (one per class). Supply either midpoints or both lower and upper, but not both.
counts	Integer vector of observed frequencies for each class. Must be the same length as midpoints (or lower/upper), all non-negative, and sum to at least 10.
lower	Numeric vector of lower interval boundaries. Required when midpoints is not supplied.
upper	Numeric vector of upper interval boundaries. Required when midpoints is not supplied. Each element must exceed the corresponding element of lower.
dists	Character vector of distribution names to fit, or "auto" (default) to use all distributions in the FitVerse registry that support MLE.
method	Fitting method: "MLE", "MOM", "LMOM", or "All" (default).
xlab	Character label for the data axis used in output summaries. Default "x".
top_n	Integer: number of top-ranked distributions to include in the printed summary. Default 5L.
verbose	Logical: print per-distribution fitting progress? Default FALSE.
file	Path to a CSV file. The file may contain comment lines beginning with #.
sep	Column separator for read_grouped_csv(). Default ",".

Details

Input formats

fitverse_grouped() accepts two input formats.

Midpoint format: Supply midpoints and counts. Interval boundaries are reconstructed by assuming equal-width classes.

Boundary format: Supply lower, upper, and counts. Classes need not be equal-width. Open-ended classes (e.g., an upper bound of Inf) are handled by replacing the infinite bound with a large finite value for midpoint computation.

Estimation

For each candidate distribution, parameters are estimated by maximising the interval-censored log-likelihood

$\ell(\theta) = \sum_{j} n_j \log\bigl[F(u_j;\theta) - F(l_j;\theta)\bigr]$

where $n_j$ is the count in class $j$, and $l_j$, $u_j$ are its lower and upper boundaries.

CSV format for read_grouped_csv()

The CSV file should have either two columns (midpoint, count) or three columns (lower, upper, count). Column names are detected automatically from a set of common variants (mid, midpoint, lower, upper, etc.). Lines starting with # are treated as comments and ignored.

Value

fitverse_grouped() returns an object of class "fitverse_grouped" containing:

results

A data frame of fitted distributions ranked by AIC, with columns for distribution name, AIC, BIC, log-likelihood, estimated parameters, and goodness-of-fit statistics.

best

The name of the best-fitting distribution.

data

A list with elements midpoints, counts, lower, and upper.

call

The matched call.

read_grouped_csv() returns a named list with elements midpoints and counts (midpoint format) or lower, upper, and counts (boundary format), ready to be passed directly to fitverse_grouped().

Author(s)

Karuna G. Reddy [email protected]
M. G. M. Khan [email protected]

See Also

fitverse for fitting to individual (ungrouped) data.
fitverse_distributions for the full distribution catalogue.

Examples

## Midpoint format
mid   <- c(5, 15, 25, 35, 45, 55, 65, 75)
count <- c(3, 12, 25, 30, 18, 8, 3, 1)
fit <- fitverse_grouped(midpoints = mid, counts = count,
                        method = "MLE", verbose = FALSE)
print(fit)

## Boundary format
low  <- c(0, 10, 20, 30, 40, 50, 60, 70)
high <- c(10, 20, 30, 40, 50, 60, 70, 80)
fit2 <- fitverse_grouped(lower = low, upper = high, counts = count,
                         method = "MLE", verbose = FALSE)
print(fit2)

## Reading from CSV
## A file with columns: lower, upper, count
tmp <- tempfile(fileext = ".csv")
writeLines(c(
  "# Example grouped data",
  "lower,upper,count",
  "0,10,5",
  "10,20,18",
  "20,30,30",
  "30,40,25",
  "40,50,12",
  "50,60,4"
), tmp)
dat <- read_grouped_csv(tmp)
fit3 <- fitverse_grouped(lower = dat$lower, upper = dat$upper,
                         counts = dat$counts)
print(fit3)

---