dWeibullgammaCount_acc: 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
)

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".

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 section ‘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.