Package 'MleCensoR' reference manual

Title:	Maximum Likelihood Estimation under Censoring Schemes
Description:	Provides generalized functions to compute Maximum Likelihood Estimation (MLE) for any univariate distribution under various censoring and truncation schemes. Users supply the probability density function (PDF), cumulative distribution function (CDF), survival function, support bounds, and initial parameter values; the package constructs and maximizes the appropriate log-likelihood automatically. Supported schemes include right and left truncation, random, right, left, interval, and middle censoring, block random censoring, balanced joint progressive Type-II (BJPT-II), progressive first failure, joint Type-I, Type-I, Type-II, progressive Type-II, Type-II progressively hybrid, joint Type-II, hybrid, hybrid Type-I, doubly Type-II, Type-I hybrid, and hybrid Type-II censoring. Optimization methods include Newton-Raphson (NR), Broyden-Fletcher-Goldfarb-Shanno (BFGS), the BFGS algorithm implemented in R (BFGSR), Berndt-Hall-Hall-Hausman (BHHH), Simulated Annealing (SANN), Conjugate Gradients (CG), and Nelder-Mead (NM). Inference summaries provide the Akaike Information Criterion (AIC), estimated coefficients, log-likelihood, iteration count, standard errors, z-values, p-values, and the variance-covariance matrix. Methods are described in Nagar, Kumar, and Krishna (2026) <doi:10.59467/IJASS.2026.22.1>, Goel, Kumar, and Krishna (2026, "Estimation in power Lindley distributions using balanced joint progressively Type-II censored data"), Wu and Kus (2009) <doi:10.1016/j.csda.2009.03.010>, Goel and Krishna (2026) <doi:10.1007/s13198-026-03208-w>, Balakrishnan and Aggarwala (2000, ISBN:978-1-4612-1334-5), Mondal and Kundu (2020) <doi:10.1080/03610926.2018.1554128>, Ding and Gui (2023) <doi:10.3390/math11092003>, Prajapati, Mitra, and Kundu (2019) <doi:10.1007/s13571-018-0167-0>, Yadav, Jaiswal, and Yadav (2026) <doi:10.1007/s11135-026-02647-8>, Iyer, Jammalamadaka, and Kundu (2008) <doi:10.1016/j.jspi.2007.03.062>, Banerjee and Kundu (2008) <doi:10.1109/TR.2008.916890>, Kundu and Joarder (2006) <doi:10.1016/j.csda.2005.05.002>, Berndt, Hall, Hall, and Hausman (1974) "Estimation and Inference in Nonlinear Structural Models" <doi:10.3386/t0003>, Fletcher (1987, "Practical Methods of Optimization", ISBN:978-0-471-91547-8), Nelder and Mead (1965) <doi:10.1093/comjnl/7.4.308>, McKinnon (1999) "Convergence of the Nelder-Mead simplex method to a non-stationary point" <doi:10.1137/S1052623496303482>, Kirkpatrick, Gelatt, and Vecchi (1983) <doi:10.1126/science.220.4598.671>, Fletcher and Reeves (1964) <doi:10.1093/comjnl/7.2.149>, and Nocedal and Wright (2006, "Numerical Optimization", ISBN:978-0-387-30303-1).
Authors:	Shikhar Tyagi [aut, cre] (ORCID: <https://orcid.org/0000-0003-1606-0844>), Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <[email protected]>
License:	GPL-3
Version:	0.1.0
Built:	2026-07-23 17:11:54 UTC
Source:	https://github.com/cran/MleCensoR

Extract Akaike Information Criterion (AIC)

Description

Extract Akaike Information Criterion (AIC)

Usage

## S3 method for class 'mle_fit'
AIC(object, ..., k = 2)
## S3 method for class 'mle_fit'
AIC(object, ..., k = 2)

Arguments

object

an object of class 'mle_fit'

...

further arguments

k

numeric, penalty per parameter (default is 2)

Value

numeric value of AIC

Extract Parameter Estimates

Description

Extract Parameter Estimates

Usage

## S3 method for class 'mle_fit'
coef(object, ...)
## S3 method for class 'mle_fit'
coef(object, ...)

Arguments

object

an object of class 'mle_fit'

...

further arguments (currently ignored)

Value

numeric vector of estimated parameters

Extract Log-Likelihood

Description

Extract Log-Likelihood

Usage

## S3 method for class 'mle_fit'
logLik(object, ...)
## S3 method for class 'mle_fit'
logLik(object, ...)

Arguments

object

an object of class 'mle_fit'

...

further arguments (currently ignored)

Value

an object of class 'logLik' with attributes "df" and "nobs"

MLE under Balanced Joint Progressive Type-II (BJPT-II) Censoring

Description

MLE under Balanced Joint Progressive Type-II (BJPT-II) Censoring

Usage

mle_bjpt2(
  w,
  z,
  D_A,
  D_B,
  pdf_A = NULL,
  cdf_A = NULL,
  surv_A = NULL,
  pdf_B = NULL,
  cdf_B = NULL,
  surv_B = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_bjpt2(
  w,
  z,
  D_A,
  D_B,
  pdf_A = NULL,
  cdf_A = NULL,
  surv_A = NULL,
  pdf_B = NULL,
  cdf_B = NULL,
  surv_B = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

w

numeric vector of failure times (ordered).

z

numeric vector indicating group membership (1 for population A, 0 for population B).

D_A

numeric vector of removals from population A at each failure time.

D_B

numeric vector of removals from population B at each failure time.

pdf_A

density function of population A.

cdf_A

cumulative distribution function of population A.

surv_A

survival function of population A (optional).

pdf_B

density function of population B (optional, defaults to pdf_A).

cdf_B

cumulative distribution function of population B (optional, defaults to cdf_A).

surv_B

survival function of population B (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Block Random Censoring

Description

MLE under Block Random Censoring

Usage

mle_block_random(
  x,
  status,
  block,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_block_random(
  x,
  status,
  block,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed values.

status

numeric vector indicating censoring status (1 = failure, 0 = censored).

block

vector indicating block/group membership for each observation.

pdf

density function of the distribution, potentially accepting a 'block' argument.

cdf

cumulative distribution function of the distribution, potentially accepting a 'block' argument.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Doubly Type-II Censoring

Description

MLE under Doubly Type-II Censoring

Usage

mle_doubly_type2(
  x,
  r,
  s,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_doubly_type2(
  x,
  r,
  s,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered).

r

integer, index of the first observed failure (1-based).

s

integer, index of the last observed failure (1-based).

n

integer, total initial units.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Hybrid Censoring (Type-I Hybrid)

Description

MLE under Hybrid Censoring (Type-I Hybrid)

Usage

mle_hybrid(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_hybrid(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered).

r

integer, target number of failures.

tc

numeric, fixed censoring time.

n

integer, total initial units.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Hybrid Type-I Censoring

Description

Alias for mle_hybrid. The experiment terminates at $T^* = \min(x_{(r)}, T_c)$ .

Usage

mle_hybrid_type1(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_hybrid_type1(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered).

r

integer, target number of failures.

tc

numeric, fixed censoring time.

n

integer, total initial units.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Hybrid Type-II Censoring

Description

MLE under Hybrid Type-II Censoring

Usage

mle_hybrid_type2(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_hybrid_type2(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered).

r

integer, target number of failures.

tc

numeric, fixed censoring time.

n

integer, total initial units.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Interval Censoring

Description

MLE under Interval Censoring

Usage

mle_interval(
  l,
  r,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_interval(
  l,
  r,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

l

numeric vector of lower bounds of the censoring intervals.

r

numeric vector of upper bounds of the censoring intervals.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Joint Type-I Censoring

Description

MLE under Joint Type-I Censoring

Usage

mle_joint_type1(
  x,
  z,
  tc,
  n_A,
  n_B,
  pdf_A = NULL,
  cdf_A = NULL,
  surv_A = NULL,
  pdf_B = NULL,
  cdf_B = NULL,
  surv_B = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_joint_type1(
  x,
  z,
  tc,
  n_A,
  n_B,
  pdf_A = NULL,
  cdf_A = NULL,
  surv_A = NULL,
  pdf_B = NULL,
  cdf_B = NULL,
  surv_B = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (<= tc) for both groups.

z

numeric vector indicating group membership (1 for population A, 0 for population B).

tc

numeric, fixed censoring time.

n_A

integer, total number of initial units in population A.

n_B

integer, total number of initial units in population B.

pdf_A

density function of population A.

cdf_A

cumulative distribution function of population A.

surv_A

survival function of population A (optional).

pdf_B

density function of population B (optional, defaults to pdf_A).

cdf_B

cumulative distribution function of population B (optional, defaults to cdf_A).

surv_B

survival function of population B (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Joint Type-II Censoring

Description

MLE under Joint Type-II Censoring

Usage

mle_joint_type2(
  w,
  z,
  n_A,
  n_B,
  pdf_A = NULL,
  cdf_A = NULL,
  surv_A = NULL,
  pdf_B = NULL,
  cdf_B = NULL,
  surv_B = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_joint_type2(
  w,
  z,
  n_A,
  n_B,
  pdf_A = NULL,
  cdf_A = NULL,
  surv_A = NULL,
  pdf_B = NULL,
  cdf_B = NULL,
  surv_B = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

w

numeric vector of observed failure times (ordered).

z

numeric vector indicating group membership (1 for population A, 0 for population B).

n_A

integer, total initial units in population A.

n_B

integer, total initial units in population B.

pdf_A

density function of population A.

cdf_A

cumulative distribution function of population A.

surv_A

survival function of population A (optional).

pdf_B

density function of population B (optional, defaults to pdf_A).

cdf_B

cumulative distribution function of population B (optional, defaults to cdf_A).

surv_B

survival function of population B (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Left Censoring

Description

MLE under Left Censoring

Usage

mle_left(
  x,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_left(
  x,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed values.

status

numeric vector indicating censoring status (1 = failure, 0 = censored).

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Left Truncation

Description

MLE under Left Truncation

Usage

mle_left_truncation(
  x,
  tl,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_left_truncation(
  x,
  tl,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed values.

tl

numeric vector or scalar of left truncation limits.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Middle Censoring

Description

MLE under Middle Censoring

Usage

mle_middle(
  x,
  u,
  v,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_middle(
  x,
  u,
  v,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed times (or NA if censored).

u

numeric vector of lower bounds of the censoring intervals.

v

numeric vector of upper bounds of the censoring intervals.

status

numeric vector indicating censoring status (1 = exact, 0 = censored).

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Progressive First Failure Censoring

Description

MLE under Progressive First Failure Censoring

Usage

mle_progressive_first_failure(
  x,
  r_removals,
  k_group_size,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_progressive_first_failure(
  x,
  r_removals,
  k_group_size,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed first-failure times (ordered).

r_removals

numeric vector of group removals at each failure time.

k_group_size

integer, number of units per group.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Type-II Progressively Hybrid Censoring

Description

Computes the MLE for any univariate distribution under the Type-II progressively hybrid censoring scheme (Kundu & Joarder, 2006). The experiment terminates at $T^* = \min(x_{(m)}, T_c)$ , where $m$ is the planned number of failures and $T_c$ is a pre-specified time limit.

Usage

mle_progressive_hybrid_type2(
  x,
  r_removals,
  tc,
  n,
  m,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_progressive_hybrid_type2(
  x,
  r_removals,
  tc,
  n,
  m,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered), only failures observed before $T^*$ .

r_removals

numeric vector of the full planned progressive removal scheme $(R_1, R_2, \ldots, R_m)$ .

tc

numeric, pre-specified time limit $T_c$ .

n

integer, total number of units initially placed on test.

m

integer, planned total number of failures (length of the full removal scheme).

pdf

density function of the distribution, accepting (x, theta, ...).

cdf

cumulative distribution function of the distribution, accepting (x, theta, ...).

surv

survival function of the distribution (optional). If not provided, computed as 1 - cdf.

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Details

The likelihood depends on whether the $m$ -th failure occurs before or after $T_c$ :

Case I ( $D = m$ , i.e., all $m$ failures observed before $T_c$ ):

$L(\theta) \propto \prod_{i=1}^{m} f(x_i; \theta) \cdot S(x_i; \theta)^{R_i}$

Case II ( $D = J < m$ , i.e., only $J$ failures observed before $T_c$ ):

$L(\theta) \propto \left[\prod_{i=1}^{J} f(x_i; \theta) \cdot S(x_i; \theta)^{R_i}\right] \cdot S(T_c; \theta)^{R_J^*}$

where $R_J^* = n - J - \sum_{i=1}^{J} R_i$ .

Value

An object of class mle_fit containing the optimization results.

References

Kundu, D., & Joarder, A. (2006). Analysis of Type-II progressively hybrid censored data. Computational Statistics & Data Analysis, 50(10), 2509-2528.

Examples


# Exponential distribution under Type-II progressively hybrid censoring
pdf_exp <- function(x, theta) dexp(x, rate = theta[1])
cdf_exp <- function(x, theta) pexp(x, rate = theta[1])

# Suppose n = 20, m = 10, tc = 2.0
# 7 failures observed before tc: Case II
x <- c(0.12, 0.35, 0.62, 0.89, 1.15, 1.48, 1.82)
r_removals <- c(1, 0, 1, 0, 1, 0, 0, 1, 0, 0)  # full plan for m = 10

fit <- mle_progressive_hybrid_type2(
  x = x, r_removals = r_removals, tc = 2.0, n = 20, m = 10,
  pdf = pdf_exp, cdf = cdf_exp,
  start = c(rate = 1.0)
)
summary(fit)

# Exponential distribution under Type-II progressively hybrid censoring
pdf_exp <- function(x, theta) dexp(x, rate = theta[1])
cdf_exp <- function(x, theta) pexp(x, rate = theta[1])

# Suppose n = 20, m = 10, tc = 2.0
# 7 failures observed before tc: Case II
x <- c(0.12, 0.35, 0.62, 0.89, 1.15, 1.48, 1.82)
r_removals <- c(1, 0, 1, 0, 1, 0, 0, 1, 0, 0)  # full plan for m = 10

fit <- mle_progressive_hybrid_type2(
  x = x, r_removals = r_removals, tc = 2.0, n = 20, m = 10,
  pdf = pdf_exp, cdf = cdf_exp,
  start = c(rate = 1.0)
)
summary(fit)

MLE under Progressive Type-II Censoring

Description

MLE under Progressive Type-II Censoring

Usage

mle_progressive_type2(
  x,
  r_removals,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_progressive_type2(
  x,
  r_removals,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered).

r_removals

numeric vector of removals at each failure time.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Random Censoring

Description

MLE under Random Censoring

Usage

mle_random(
  x,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_random(
  x,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed values.

status

numeric vector indicating censoring status (1 = failure, 0 = censored).

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Right Censoring

Description

MLE under Right Censoring

Usage

mle_right(
  x,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_right(
  x,
  status,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed values.

status

numeric vector indicating censoring status (1 = failure, 0 = censored).

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Right Truncation

Description

MLE under Right Truncation

Usage

mle_right_truncation(
  x,
  tr,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_right_truncation(
  x,
  tr,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed values.

tr

numeric vector or scalar of right truncation limits.

pdf

density function of the distribution, accepting '(x, theta, ...)'.

cdf

cumulative distribution function of the distribution, accepting '(x, theta, ...)'.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Type-I Censoring

Description

MLE under Type-I Censoring

Usage

mle_type1(
  x,
  tc,
  status = NULL,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_type1(
  x,
  tc,
  status = NULL,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed values.

tc

numeric, fixed censoring time.

status

numeric vector indicating censoring status (optional, determined as x < tc if NULL).

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Type-I Hybrid Censoring

Description

Alias for mle_hybrid. The experiment terminates at $T^* = \min(x_{(r)}, T_c)$ .

Usage

mle_type1_hybrid(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_type1_hybrid(
  x,
  r,
  tc,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered).

r

integer, target number of failures.

tc

numeric, fixed censoring time.

n

integer, total initial units.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

MLE under Type-II Censoring

Description

MLE under Type-II Censoring

Usage

mle_type2(
  x,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)
mle_type2(
  x,
  n,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start,
  method = NULL,
  constraints = NULL,
  grad = NULL,
  hess = NULL,
  param_range = NULL,
  logLik = NULL,
  ...
)

Arguments

x

numeric vector of observed failure times (ordered).

n

integer, total number of units in the experiment.

pdf

density function of the distribution.

cdf

cumulative distribution function of the distribution.

surv

survival function of the distribution (optional).

start

numeric vector of initial parameter values.

method

character string, optimization method.

constraints

list, optimization constraints.

grad

gradient function.

hess

Hessian function.

param_range

list, parameter ranges.

logLik

custom log-likelihood function.

...

further arguments passed to optimization or user-defined functions.

Value

An object of class 'mle_fit' containing the optimization results.

Extract Number of Iterations

Description

Extract Number of Iterations

Usage

nIter(x, ...)
nIter(x, ...)

Arguments

x

an object of class 'mle_fit'

...

further arguments (currently ignored)

Value

integer representing number of iterations

Print MLE Fit

Description

Print MLE Fit

Usage

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

Arguments

x

an object of class 'mle_fit'

...

further arguments (currently ignored)

Value

The input object x is returned invisibly. Called for its side effect of printing estimated parameters and the log-likelihood value to the console.

Print Summary Table

Description

Print Summary Table

Usage

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

Arguments

x

an object of class 'summary.mle_fit'

...

further arguments (currently ignored)

Value

The input object x is returned invisibly. Called for its side effect of printing a formatted summary table to the console.

Extract Standard Errors

Description

Extract Standard Errors

Usage

stdEr(x, ...)
stdEr(x, ...)

Arguments

x

an object of class 'mle_fit'

...

further arguments (currently ignored)

Value

numeric vector of standard errors

Summarize MLE Fit

Description

Summarize MLE Fit

Usage

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

Arguments

object

an object of class 'mle_fit'

...

further arguments (currently ignored)

Value

summary.mle_fit object

Extract Variance-Covariance Matrix

Description

Extract Variance-Covariance Matrix

Usage

## S3 method for class 'mle_fit'
vcov(object, ...)
## S3 method for class 'mle_fit'
vcov(object, ...)

Arguments

object

an object of class 'mle_fit'

...

further arguments (currently ignored)

Value

variance-covariance matrix

Package 'MleCensoR'

Help Index

Extract Akaike Information Criterion (AIC)

Description

Usage

Arguments

Value

Extract Parameter Estimates

Description

Usage

Arguments

Value

Extract Log-Likelihood

Description

Usage

Arguments

Value

MLE under Balanced Joint Progressive Type-II (BJPT-II) Censoring

Description

Usage

Arguments

Value

MLE under Block Random Censoring

Description

Usage

Arguments

Value

MLE under Doubly Type-II Censoring

Description

Usage

Arguments

Value

MLE under Hybrid Censoring (Type-I Hybrid)

Description

Usage

Arguments

Value

MLE under Hybrid Type-I Censoring

Description

Usage

Arguments

Value

MLE under Hybrid Type-II Censoring

Description

Usage

Arguments

Value

MLE under Interval Censoring

Description

Usage

Arguments

Value

MLE under Joint Type-I Censoring

Description

Usage

Arguments

Value

MLE under Joint Type-II Censoring

Description

Usage

Arguments

Value

MLE under Left Censoring

Description

Usage

Arguments

Value

MLE under Left Truncation

Description

Usage

Arguments

Value

MLE under Middle Censoring

Description

Usage

Arguments

Value

MLE under Progressive First Failure Censoring

Description

Usage