Probability calculations for Weibull count models

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.

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.

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.

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.