dWeibullgammaCount: Fast Univariate Weibull Count Probability with gamma...

In GeoBosh/Countr: Flexible Univariate Count Models Based on Renewal Processes

Fast Univariate Weibull Count Probability with gamma heterogeneity

Description

Probability computations for the univariate Weibull-gamma count processes. Several methods are provided. dWeibullgammaCount computes probabilities.

dWeibullgammaCount_loglik computes the log-likelihood.

evWeibullgammaCount computes the expected value and variance.

Usage

dWeibullgammaCount_acc(
  x,
  shape,
  r,
  alpha,
  time = 1,
  logFlag = FALSE,
  jmax = 100L,
  nmax = 300L,
  eps = 1e-10,
  printa = FALSE
)

dWeibullgammaCount(
  x,
  shape,
  shapeGam,
  scaleGam,
  Xcovar = NULL,
  beta = NULL,
  method = c("series_acc", "series_mat"),
  time = 1,
  log = FALSE,
  series_terms = 50,
  series_acc_niter = 300,
  series_acc_eps = 1e-10
)

dWeibullgammaCount_loglik(
  x,
  shape,
  shapeGam,
  scaleGam,
  Xcovar = NULL,
  beta = NULL,
  method = c("series_acc", "series_mat"),
  time = 1,
  na.rm = TRUE,
  series_terms = 50,
  series_acc_niter = 300,
  series_acc_eps = 1e-10,
  weights = NULL
)

evWeibullgammaCount(
  xmax,
  shape,
  shapeGam,
  scaleGam,
  Xcovar = NULL,
  beta = NULL,
  method = c("series_acc", "series_mat"),
  time = 1,
  series_terms = 50,
  series_acc_niter = 300,
  series_acc_eps = 1e-10
)

Arguments

x	integer (vector), the desired count values.
shape	numeric (length 1), shape parameter of the Weibull count.
r	numeric shape of the gamma distribution
alpha	numeric rate of the gamma distribution
time	double, length of the observation window (defaults to 1).
logFlag	logical, if TRUE, the log of the probability will be returned.
jmax	integer, number of terms used to approximate the (infinite) series.
nmax	integer, an upper bound on the number of terms to be summed in the Euler-van Wijngaarden sum; default is 300 terms.
eps	numeric, the desired accuracy to declare convergence.
printa	logical, if TRUE print information about convergence.
shapeGam, scaleGam	numeric shape and scale parameters of the gamma heterogeity function.
Xcovar	matrix the regressor values. Should have the same number of rows as length(x). If NULL, no regression will be considered.
beta	numeric regression coefficients. If NULL, no regression will be considered.
method	character one of the available methods. See details.
log	logical, if TRUE, the log of the probability will be returned.
series_terms	numeric number of terms in the series expansion.
series_acc_niter	numeric number of iteration in the Euler-van Wijngaarden algorithm.
series_acc_eps	numeric tolerance of convergence in the Euler-van Wijngaarden algorithm.
na.rm	logical, if TRUE, NA's (produced by taking the log of very small probabilities) will be replaced by the smallest allowed probaility; default = TRUE.
weights	numeric, vector of weights to apply. If NULL, one will be applied.
xmax	unsigned integer, maximum count to be used.

Details

The desired method can be specified by argument method, as follows:

"series_mat"

series expansion using matrix techniques.

"series_acc"

Euler-van Wijngaarden accelerated series expansion.

The arguments have sensible default values.

Value

for dWeibullgammaCount, a vector of probabilities P(x(i)), i = 1, \dots n where n = length(x).

for dWeibullgammaCount_loglik, double, log-likelihood of the count process

for evWeibullgammaCount, a list with components "ExpectedValue" and "Variance".

GeoBosh/Countr documentation built on Jan. 26, 2024, 12:16 p.m.