dWeibullCount: Probability calculations for Weibull count models

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

Probability calculations for Weibull count models

Description

Probability computations for the univariate Weibull count process. Several methods are provided. dWeibullCount computes probabilities.

dWeibullCount_loglik computes the log-likelihood.

evWeibullCount computes the expected value and variance.

Usage

dWeibullCount(
  x,
  shape,
  scale,
  method = c("series_acc", "series_mat", "conv_direct", "conv_naive", "conv_dePril"),
  time = 1,
  log = FALSE,
  conv_steps = 100,
  conv_extrap = TRUE,
  series_terms = 50,
  series_acc_niter = 300,
  series_acc_eps = 1e-10
)

dWeibullCount_loglik(
  x,
  shape,
  scale,
  method = c("series_acc", "series_mat", "conv_direct", "conv_naive", "conv_dePril"),
  time = 1,
  na.rm = TRUE,
  conv_steps = 100,
  conv_extrap = TRUE,
  series_terms = 50,
  series_acc_niter = 300,
  series_acc_eps = 1e-10,
  weights = NULL
)

evWeibullCount(
  xmax,
  shape,
  scale,
  method = c("series_acc", "series_mat", "conv_direct", "conv_naive", "conv_dePril"),
  time = 1,
  conv_steps = 100,
  conv_extrap = TRUE,
  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.
scale	numeric (length 1), scale parameter of the Weibull count.
method	character, one of the available methods, see details.
time	double, length of the observation window (defaults to 1).
log	logical, if TRUE, the log of the probability will be returned.
conv_steps	numeric, number of steps used for the extrapolation.
conv_extrap	logical, should Richardson extrappolation be applied ?
series_terms	numeric, number of terms in the series expansion.
series_acc_niter	numeric, number of iterations 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 is TRUE.
weights	numeric, vector of weights to apply. If NULL, a vector of one's will be applied.
xmax	unsigned integer, maximum count to be used.

Details

Argument method can be used to specify the desired method, as follows:

"series_mat"

- series expansion using matrix techniques,

"series_acc"

- Euler-van Wijngaarden accelerated series expansion (default),

"conv_direc"t

- direct convolution method of section 2,

"conv_naive"

- naive convolurion described in section 3.1,

"conv_dePril"

- dePril convolution described in section 3.2.

The arguments have sensible default values.

Value

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

for dWeibullCount_loglik, a double, the log-likelihood of the count process.

for evWeibullCount, a list with components:

ExpectedValue	expected value,
Variance	variance.

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