dWeibullCount_mat: Univariate Weibull Count Probability

In Countr: Flexible Univariate Count Models Based on Renewal Processes

Univariate Weibull Count Probability

Description

Univariate Weibull count probability computed using matrix techniques.

Usage

dWeibullCount_mat(x, shape, scale, time = 1, logFlag = FALSE, jmax = 50L)

dWeibullCount_acc(
  x,
  shape,
  scale,
  time = 1,
  logFlag = FALSE,
  jmax = 50L,
  nmax = 300L,
  eps = 1e-10,
  printa = FALSE
)

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.
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.

Details

dWeibullCount_mat implements formulae (11) of McShane(2008) to compute the required probabilities. For speed, the computations are implemented in C++ and of matrix computations are used whenever possible. This implementation is not efficient as it recomputes the alpha matrix each time, which may slow down computation (among other things).

dWeibullCount_acc achieves a vast (several orders of magnitude) speed improvement over pWeibullCountOrig. We achieve this by using Euler-van Wijngaarden techniques for accelerating the convergence of alternating series and tabulation of the alpha terms available in a pre-computed matrix (shipped with the package).

When computation time is an issue, we recommend the use of dWeibullCount_fast. However, pWeibullCountOrig may be more accurate, especially when jmax is large.

Value

a vector of probabilities for each component of the count vector x.

Countr documentation built on Nov. 13, 2022, 1:06 a.m.