Package 'nhppp'

Generic function for simulating from NHPPPs given the intensity function or the cumulative intensity function.

Description

This is a wrapper to the package's specific functions, and thus somewhat slower. For time-intensive simulations prefer one of the specific functions.

Usage

draw(
  Lambda = NULL,
  Lambda_inv = NULL,
  lambda = NULL,
  line_majorizer_intercept = NULL,
  line_majorizer_slope = NULL,
  line_majorizer_is_loglinear = FALSE,
  step_majorizer_vector = NULL,
  t_min = NULL,
  t_max = NULL,
  atmost1 = FALSE,
  atleast1 = FALSE
)

Arguments

Lambda	(function, double vector) the integrated (cumulative) rate of the NHPPP
Lambda_inv	(function, double vector) the inverse of ‘Lambda()’
lambda	(function) the instantaneous rate
line_majorizer_intercept	The intercept alpha of the loglinear majorizer function: alpha + beta * t or exp(alpha + beta * t)
line_majorizer_slope	The slope beta of the loglinear majorizer function: alpha + beta * t or exp(alpha + beta * t)
line_majorizer_is_loglinear	(boolean) if TRUE the majorizer is loglinear exp(alpha + beta * t); if FALSE it is a linear function
step_majorizer_vector	(vector, double) K constant majorizing rates, one per interval; all intervals are of equal length (regular)
t_min	(double) the lower bound of the interval
t_max	(double) the upper bound of the interval
atmost1	boolean, draw at most 1 event time
atleast1	boolean, draw at least 1 event time in interval

Value

a vector of event times

---

Simulate from a non homogeneous Poisson Point Process (NHPPP) over an interval when you know the cumulative intensity and its inverse.

Description

Sample NHPPP times using the inversion method

Usage

draw_cumulative_intensity(Lambda, Lambda_inv, t_min, t_max, atmost1 = FALSE)

Arguments

Lambda	(function, double vector) a continuous increasing R to R map which is the integrated rate of the NHPPP
Lambda_inv	(function, double vector) the inverse of Lambda()
t_min	(double) the lower bound of the time interval
t_max	(double) the upper bound of the time interval
atmost1	boolean, draw at most 1 event time

Value

a vector of event times (t_); if no events realize, a vector of length 0

---

Generic function for simulating from NHPPPs given the intensity function.

Description

Sample from NHPPPs given the intensity function This is a wrapper to the package's specific functions, and thus somewhat slower. For time-intensive simulations prefer one of the specific functions.

Usage

draw_intensity(
  lambda,
  line_majorizer_intercept = NULL,
  line_majorizer_slope = NULL,
  line_majorizer_is_loglinear = FALSE,
  step_majorizer_vector = NULL,
  t_min = NULL,
  t_max = NULL,
  atmost1 = FALSE
)

Arguments

lambda	(function) the instantaneous rate
line_majorizer_intercept	The intercept alpha of the loglinear majorizer function: alpha + beta * t or exp(alpha + beta * t)
line_majorizer_slope	The slope beta of the loglinear majorizer function: alpha + beta * t or exp(alpha + beta * t)
line_majorizer_is_loglinear	(boolean) if TRUE the majorizer is loglinear exp(alpha + beta * t); if FALSE it is a linear function
step_majorizer_vector	(vector, double) K constant majorizing rates, one per interval; all intervals are of equal length (regular)
t_min	(double) the lower bound of the interval
t_max	(double) the upper bound of the interval
atmost1	boolean, draw at most 1 event time

Value

a vector of event times

---

Special case: Simulate from a non homogeneous Poisson Point Process (NHPPP) from (t_min, t_max) with linear intensity function (inversion method)

Description

Sample NHPPP times from a linear intensity function using the inversion method, optionally using an rstream generator

Usage

draw_sc_linear(intercept, slope, t_min, t_max, atmost1 = FALSE)

Arguments

intercept	(double) the intercept
slope	(double) the slope
t_min	(double) lower bound of the time interval
t_max	(double) upper bound of the time interval
atmost1	boolean, draw at most 1 event time

Value

a vector of event times (t_); if no events realize, a vector of length 0

Examples

x <- draw_sc_linear(intercept = 0, slope = 0.2, t_min = 0, t_max = 10)

---

Special case: Simulate from a non homogeneous Poisson Point Process (NHPPP) from (t_min, t_max) with log-linear intensity function (inversion method)

Description

Sample NHPPP times from an log linear intensity function using the inversion method, optionally using an rstream generator

Usage

draw_sc_loglinear(intercept, slope, t_min, t_max, atmost1 = FALSE)

Arguments

intercept	(double) the intercept in the exponent
slope	(double) the slope in the exponent
t_min	(double) lower bound of the time interval
t_max	(double) upper bound of the time interval
atmost1	boolean, draw at most 1 event time

Value

a vector of event times (t_); if no events realize, a vector of length 0

Examples

x <- draw_sc_loglinear(intercept = 0, slope = 0.2, t_min = 0, t_max = 10)

---

Simulate a piecewise constant-rate Poisson Point Process over ⁠(t_min, t_max]⁠ (inversion method) The intervals need not have the same length.

Description

Simulate a piecewise constant-rate Poisson Point Process over ⁠(t_min, t_max]⁠ (inversion method) The intervals need not have the same length.

Usage

draw_sc_step(lambda_vector, time_breaks, atmost1 = FALSE, atleast1 = FALSE)

Arguments

lambda_vector	(scalar, double) K constant rates, one per interval
time_breaks	(vector, double) K+1 time points defining K intervals of constant rates: ⁠[t_1 = range_t[1], t_2)⁠: the first interval ⁠[t_k, t_{k+1})⁠: the k-th interval ⁠[t_{K}, t_{K+1} = range_t[2])⁠: the K-th (last) interval
atmost1	boolean, draw at most 1 event time
atleast1	boolean, draw at least 1 event time

Value

a vector of event times t if no events realize, it will have 0 length

Examples

x <- draw_sc_step(lambda_vector = rep(1, 5), time_breaks = c(0:5))

---

Sampling from NHPPPs with piecewise constant intensities with same interval lengths (non-vectorized)

Description

Sampling from NHPPPs with piecewise constant intensities with same interval lengths (non-vectorized)

Usage

draw_sc_step_regular(
  Lambda_vector = NULL,
  lambda_vector = NULL,
  t_min = NULL,
  t_max = NULL,
  atmost1 = FALSE,
  atleast1 = FALSE
)

Arguments

Lambda_vector	(scalar, double) K integrated intensity rates at the end of each interval
lambda_vector	(scalar, double) K constant intensity rates, one per interval
t_min	(scalar, double) lower bound of the time interval
t_max	(scalar, double) upper bound of the time interval
atmost1	boolean, draw at most 1 event time
atleast1	boolean, draw at least 1 event time

Value

a vector of event times t if no events realize, it will have 0 length

Examples

x <- draw_sc_step_regular(Lambda_vector = 1:5, t_min = 0, t_max = 5)

---

Piecewise constant (step) majorizer for K-Lipschitz functions over an interval (vectorized over the breaks argument).

Description

Return a piecewise constant (step) majorizer for K-Lipschitz functions over an interval. The function is vectorized over the breaks argument.

Usage

get_step_majorizer(fun, breaks, is_monotone = TRUE, K = 0)

Arguments

fun	A function object with a single argument x. If x is a matrix, fun should be vectorized over it.
breaks	(vector or matrix) The set of M+1 boundaries for the M subintervals in x. If breaks is a matrix, each row is treated as a separate set of breaks.
is_monotone	(boolean) Is the function monotone? (Default is TRUE.)
K	(double) A non-negative number for the Lipschitz cone. (Default is 0.)

Value

A vector of length M with the values of the piecewise constant majorizer

Examples

get_step_majorizer(fun = abs, breaks = -5:5, is_monotone = FALSE, K = 1)

---

Simulate a homogeneous Poisson Point Process in (t_min, t_max]

Description

Simulate a homogeneous Poisson Point Process in (t_min, t_max]

Usage

ppp(rate, t_min, t_max, atmost1 = FALSE, tol = 10^-6)

Arguments

rate	(scalar, double) constant instantaneous rate
t_min	(scalar, double) the lower bound of the time interval
t_max	(scalar, double) the upper bound of the time interval
atmost1	boolean, draw at most 1 event time
tol	the probability that we will have more than the drawn events in (t_min, t_max]

Value

a vector of event times t if no events realize, it will have 0 length

Examples

x <- ppp(rate = 1, t_min = 0, t_max = 10, tol = 10^-6)

---

Simulate exactly n points from a homogeneous Poisson Point Process over (t_min, t_max]

Description

Simulate exactly n points from a homogeneous Poisson Point Process over (t_min, t_max]

Usage

ppp_exactly_n(n, t_min, t_max)

Arguments

n	(int) the number of points to be simulated
t_min	(double) the lower bound of the time interval
t_max	(double) the upper bound of the time interval

Value

a vector of event times of size n

Examples

x <- ppp_exactly_n(n = 10, t_min = 0, t_max = 10)

---

Simulate n events from a homogeneous Poisson Point Process.

Description

Simulate n events from a homogeneous Poisson Point Process.

Usage

ppp_next_n(n = 1, rate = 1, t_min = 0, rng_stream = deprecated())

Arguments

n	scalar number of samples
rate	scalar instantaneous rate
t_min	scalar for the starting time value
rng_stream	an rstream object

Value

a vector with event times t (starting from t_min)

Examples

x <- ppp_next_n(n = 10, rate = 1, t_min = 0)

---

Vectorized generic function for simulating from NHPPPs given the intensity function or the cumulative intensity function

Description

This is a wrapper to the package's specific functions, and thus slightly slower. For time-intensive simulations prefer one of the specific functions.

Usage

vdraw(
  lambda = NULL,
  lambda_args = NULL,
  Lambda_maj_matrix = NULL,
  lambda_maj_matrix = NULL,
  Lambda = NULL,
  Lambda_inv = NULL,
  Lambda_args = NULL,
  Lambda_inv_args = NULL,
  t_min = NULL,
  t_max = NULL,
  rate_matrix_t_min = NULL,
  rate_matrix_t_max = NULL,
  tol = 10^-6,
  atmost1 = FALSE,
  atleast1 = FALSE,
  atmostB = NULL
)

Arguments

lambda	(function) intensity function, vectorized
lambda_args	(list) optional arguments to pass to lambda
Lambda_maj_matrix	(matrix) integrated intensity rates at the end of each interval
lambda_maj_matrix	(matrix) intensity rates, one per interval
Lambda	(function, double vector) an increasing function which is the integrated rate of the NHPPP. It should take a vectorized argument t for times and an optional arguments list.
Lambda_inv	(function, double vector) the inverse of Lambda(), also in vectorized form It should take a vectorized argument z and an optional arguments list.
Lambda_args	(list) optional arguments to pass to Lambda.
Lambda_inv_args	(list) optional arguments to pass to Lambda_inv().
t_min	(scalar | vector | column matrix) is the lower bound of a subinterval of (rate_matrix_t_min, rate_matrix_t_max]. If set, times are sampled from the subinterval. If omitted, it is equivalent to rate_matrix_t_min.
t_max	(scalar | vector | column matrix) is the upper bound of a subinterval of (rate_matrix_t_min, rate_matrix_t_max]. If set, times are sampled from the subinterval. If omitted, it is equivalent to rate_matrix_t_max.
rate_matrix_t_min	(scalar | vector | column matrix) is the lower bound of the time interval for each row of (Lambda|lambda)_maj_matrix. The length of this argument is the number of point processes that should be drawn.
rate_matrix_t_max	(scalar | vector | column matrix) the upper bound of the time interval for each row of (Lambda|lambda)_maj_matrix. The length of this argument is the number of point processes that should be drawn.
tol	(scalar, double) tolerance for the number of events
atmost1	boolean, draw at most 1 event time
atleast1	boolean, draw at least 1 event time
atmostB	If not NULL, draw at most B (B>0) event times. NULL means ignore.

Value

a vector of event times

---

Vectorized simulation from a non homogeneous Poisson Point Process (NHPPP) from (t_min, t_max) given the cumulative intensity function and its inverse

Description

Sample NHPPP times using the cumulative intensity function and its inverse.

Usage

vdraw_cumulative_intensity(
  Lambda,
  Lambda_inv,
  t_min,
  t_max,
  Lambda_args = NULL,
  Lambda_inv_args = NULL,
  tol = 10^-6,
  atmost1 = FALSE,
  atleast1 = FALSE
)

Arguments

Lambda	(function, double vector) an increasing function which is the integrated rate of the NHPPP. It should take a vectorized argument t for times and an optional arguments list.
Lambda_inv	(function, double vector) the inverse of Lambda(), also in vectorized form It should take a vectorized argument z and an optional arguments list.
t_min	(scalar | vector | column matrix) the lower bound of the interval for each sampled point process The length of this argument is the number of point processes that should be drawn.
t_max	(scalar | vector | column matrix) the upper bound of the interval for each sampled point process The length of this argument is the number of point processes that should be drawn.
Lambda_args	(list) optional arguments to pass to Lambda.
Lambda_inv_args	(list) optional arguments to pass to Lambda_inv().
tol	the tolerange for the calulations.
atmost1	boolean, draw at most 1 event time per sampled point process.
atleast1	boolean, draw at least 1 event time

Value

a matrix of event times with one row per sampled point process.

---

Vectorized sampling from a non homogeneous Poisson Point Process (NHPPP) from an interval (thinning method) with piecewise constant_majorizers (C++)

Description

Vectorized sampling from a non homogeneous Poisson Point Process (NHPPP) from an interval (thinning method) with piecewise constant_majorizers. The majorizers are step functions over equal-length time intevals.

Usage

vdraw_intensity(
  lambda = NULL,
  lambda_args = NULL,
  Lambda_maj_matrix = NULL,
  lambda_maj_matrix = NULL,
  rate_matrix_t_min = NULL,
  rate_matrix_t_max = NULL,
  t_min = NULL,
  t_max = NULL,
  tol = 10^-6,
  atmost1 = FALSE,
  atleast1 = FALSE,
  atmostB = NULL
)

Arguments

lambda	(function) intensity function, vectorized
lambda_args	(list) optional arguments to pass to lambda
Lambda_maj_matrix	(matrix) integrated intensity rates at the end of each interval
lambda_maj_matrix	(matrix) intensity rates, one per interval
rate_matrix_t_min	(scalar | vector | column matrix) is the lower bound of the time interval for each row of (Lambda|lambda)_maj_matrix. The length of this argument is the number of point processes that should be drawn.
rate_matrix_t_max	(scalar | vector | column matrix) the upper bound of the time interval for each row of (Lambda|lambda)_maj_matrix. The length of this argument is the number of point processes that should be drawn.
t_min	(scalar | vector | column matrix) is the lower bound of a subinterval of (rate_matrix_t_min, rate_matrix_t_max]. If set, times are sampled from the subinterval. If omitted, it is equivalent to rate_matrix_t_min.
t_max	(scalar | vector | column matrix) is the upper bound of a subinterval of (rate_matrix_t_min, rate_matrix_t_max]. If set, times are sampled from the subinterval. If omitted, it is equivalent to rate_matrix_t_max.
tol	(scalar, double) tolerance for the number of events
atmost1	boolean, draw at most 1 event time
atleast1	boolean, draw at least 1 event time
atmostB	If not NULL, draw at most B (B>0) event times. NULL means ignore.

Value

a matrix of event times (columns) per draw (rows) NAs are structural empty spots

Examples

x <- vdraw_intensity(
  lambda = function(x, ...) 0.1 * x,
  lambda_maj_matrix = matrix(rep(1, 5), nrow = 1),
  rate_matrix_t_min = 1,
  rate_matrix_t_max = 5
)

---

Vectorized sampling from NHPPPs with piecewise constant intensities with same interval lengths

Description

Simulate a piecewise constant-rate Poisson Point Process over ⁠(t_min, t_max]⁠ (inversion method) where the intervals have the same length (are "regular").

Usage

vdraw_sc_step_regular(
  lambda_matrix = NULL,
  Lambda_matrix = NULL,
  rate_matrix_t_min = NULL,
  rate_matrix_t_max = NULL,
  t_min = NULL,
  t_max = NULL,
  tol = 10^-6,
  atmost1 = FALSE,
  atmostB = NULL,
  atleast1 = FALSE
)

Arguments

lambda_matrix	(matrix) intensity rates, one per interval
Lambda_matrix	(matrix) integrated intensity rates at the end of each interval
rate_matrix_t_min	(scalar | vector | column matrix) is the lower bound of the time interval for each row of (Lambda|lambda)_maj_matrix. The length of this argument is the number of point processes that should be drawn.
rate_matrix_t_max	(scalar | vector | column matrix) the upper bound of the time interval for each row of (Lambda|lambda)_maj_matrix. The length of this argument is the number of point processes that should be drawn.
t_min	(scalar | vector | column matrix) is the lower bound of a subinterval of (rate_matrix_t_min, rate_matrix_t_max]. If set, times are sampled from the subinterval. If omitted, it is equivalent to rate_matrix_t_min.
t_max	(scalar | vector | column matrix) is the upper bound of a subinterval of (rate_matrix_t_min, rate_matrix_t_max]. If set, times are sampled from the subinterval. If omitted, it is equivalent to rate_matrix_t_max.
tol	(scalar, double) tolerance for the number of events
atmost1	boolean, draw at most 1 event time
atmostB	If not NULL, draw at most B (B>0) event times. NULL means ignore.
atleast1	boolean, draw at least 1 event time

Value

a vector of event times t if no events realize, it will have 0 length

Examples

x <- vdraw_sc_step_regular(
  Lambda_matrix = matrix(1:5, nrow = 1),
  rate_matrix_t_min = 100,
  rate_matrix_t_max = 110,
  atmost1 = FALSE
)

---

Simulate from a zero-truncated non homogeneous Poisson Point Process (zt-NHPPP) from (t_min, t_max) (order statistics method)

Description

Sample zero-truncated NHPPP times using the order statistics method, optionally using an rstream generator

Usage

ztdraw_cumulative_intensity(Lambda, Lambda_inv, t_min, t_max, atmost1 = FALSE)

Arguments

Lambda	(function, double vector) a continuous increasing R to R map which is the integrated rate of the NHPPP
Lambda_inv	(function, double vector) the inverse of Lambda()
t_min	(double) the lower bound of the time interval
t_max	(double) the upper bound of the time interval
atmost1	(boolean) draw at most 1 event time

Value

a vector of at least 1 event times

---

Simulate size samples from a zero-truncated non homogeneous Poisson Point Process (zt-NHPPP) from (t_min, t_max) with linear intensity function

Description

Sample zero-truncated NHPPP times from a linear intensity function using the inversion method, optionally using an rstream generator

Usage

ztdraw_sc_linear(intercept, slope, t_min, t_max, atmost1 = FALSE)

Arguments

intercept	(double) the intercept
slope	(double) the slope
t_min	(double) the lower bound of the time interval
t_max	(double) the upper bound of the time interval
atmost1	(boolean) draw 1 event time

Value

a vector of at least 1 event times

Examples

x <- ztdraw_sc_linear(intercept = 0, slope = 0.2, t_min = 0, t_max = 10)

---

Simulate from a zero-truncated non homogeneous Poisson Point Process (zt-NHPPP) from (t_min, t_max) with a log-linear intensity function

Description

Sample zt-NHPPP times from an log-linear intensity function

Usage

ztdraw_sc_loglinear(intercept, slope, t_min, t_max, atmost1 = FALSE)

Arguments

intercept	(double) the intercept in the exponent
slope	(double) the slope in the exponent
t_min	(double) the lower bound of the time interval
t_max	(double) the upper bound of the time interval
atmost1	boolean, 1 event time

Value

a vector of at least 1 event times

Examples

x <- ztdraw_sc_loglinear(intercept = 0, slope = 0.2, t_min = 0, t_max = 10)

---

Simulate a zero-truncated homogeneous Poisson Point Process over (t_min, t_max]

Description

Simulate a zero-truncated homogeneous Poisson Point Process over (t_min, t_max]

Usage

ztppp(rate, t_min, t_max, atmost1 = FALSE)

Arguments

rate	(scalar, double) constant instantaneous rate
t_min	(scalar, double) lower bound of the time interval
t_max	(scalar, double) upper bound of the time interval
atmost1	boolean, draw at most 1 event time

Value

a vector of event times of size size

Examples

x <- ztppp(t_min = 0, t_max = 10, rate = 0.001)

---