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

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.

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

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)
#> [1] -40.52531

dCount_conv_loglik_user(x, distParsList, extrapolParsList,
                        pwei_user, "direct", nsteps = 400)
#> [1] -40.52531

## log-likehood naive Poisson
dCount_conv_loglik_bi(x, distParsList,
                      "weibull", "naive", nsteps = 400)
#> [1] -40.52531

dCount_conv_loglik_user(x, distParsList, extrapolParsList,
                        pwei_user, "naive", nsteps = 400)
#> [1] -40.52531

## log-likehood dePril Poisson
dCount_conv_loglik_bi(x, distParsList,
                      "weibull", "dePril", nsteps = 400)
#> [1] -40.52531

dCount_conv_loglik_user(x, distParsList, extrapolParsList,
                        pwei_user, "dePril", nsteps = 400)
#> [1] -40.52531
## see dCount_conv_loglik_bi()