Log-likelihood of a count probability computed by convolution (bi)

Description

Compute the log-likelihood of a count model using convolution methods to compute the probabilities. dCount_conv_loglik_bi is for the builtin distributions. dCount_conv_loglik_user is for user defined survival functions.

Usage

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dCount_conv_loglik_bi(x, distPars, dist = c("weibull", "gamma", "gengamma",
  "burr"), method = c("dePril", "direct", "naive"), nsteps = 100,
  time = 1, extrap = TRUE, na.rm = TRUE, weights = NULL)

dCount_conv_loglik_user(x, distPars, extrapolPars, survR, method = c("dePril",
  "direct", "naive"), nsteps = 100, time = 1, extrap = TRUE,
  na.rm = TRUE, weights = NULL)

Arguments

x

integer (vector), the desired count values.

distPars

list of the same length as x with each slot being itself a named list containing the distribution parameters corresponding to x[i].

dist

character name of the built-in distribution, see details.

method

character, convolution method to be used; choices are "dePril" (section 3.2), "direct" (section 2) or "naive" (section 3.1).

nsteps

unsiged integer number of steps used to compute the integral.

time

double time at wich to compute the probabilities. Set to 1 by default.

extrap

logical if TRUE, Richardson extrapolation will be applied to improve accuracy.

na.rm

logical, if TRUE, NAs (produced by taking the log of very small probabilities) will be replaced by the smallest allowed probability; default is TRUE.

weights

numeric, vector of weights to apply. If NULL, a vector of ones.

extrapolPars

list of same length as x where each slot is a vector of length 2 (the extrapolation values to be used) corresponding to x[i].

survR

a user defined survival function; should have the signature function(t, distPars) where t is a real number (>0) where the survival function is evaluated and distPars is a list of distribution parameters. It should return a double value.

Value

numeric, the log-likelihood of the count process

Examples

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x <- 0:10
lambda <- 2.56
distPars <- list(scale = lambda, shape = 1)
distParsList <- lapply(seq(along = x), function(ind) distPars)
extrapolParsList <- lapply(seq(along = x), function(ind) c(2, 1))
## user pwei
pwei_user <- function(tt, distP) {
    alpha <- exp(-log(distP[["scale"]]) / distP[["shape"]])
    pweibull(q = tt, scale = alpha, shape = distP[["shape"]],
             lower.tail = FALSE)
}

## log-likehood allProbs Poisson
dCount_conv_loglik_bi(x, distParsList,
                      "weibull", "direct", nsteps = 400)

dCount_conv_loglik_user(x, distParsList, extrapolParsList,
                        pwei_user, "direct", nsteps = 400)

## log-likehood naive Poisson
dCount_conv_loglik_bi(x, distParsList,
                      "weibull", "naive", nsteps = 400)

dCount_conv_loglik_user(x, distParsList, extrapolParsList,
                        pwei_user, "naive", nsteps = 400)

## log-likehood dePril Poisson
dCount_conv_loglik_bi(x, distParsList,
                      "weibull", "dePril", nsteps = 400)

dCount_conv_loglik_user(x, distParsList, extrapolParsList,
                        pwei_user, "dePril", nsteps = 400)
## see dCount_conv_loglik_bi()

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