Probability calculations for Weibull count models

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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

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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, … 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.

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