R/Logarithmic.R

In actuar: Actuarial Functions and Heavy Tailed Distributions

### actuar: Actuarial Functions and Heavy Tailed Distributions
###
### Definition of the {d,p,r}logarithmic functions to compute
### characteristics of the logarithmic distribution. The version used
### in these functions has probability mass function
###
###   Pr[X = x] = -p^x/(x log(1 - p)), x = 1, 2, ...
###
### This is the standard parametrization in the literature; see for
### example https://en.wikipedia.org/wiki/Logarithmic_distribution.
###
### NOTE: Klugman, Panjer & Willmot (Loss Models) introduce the
### logarithmic distribution as a limiting case of the zero truncated
### negative binomial. In this setting, parameter 'p' above would be
### the probability of *failure* (a.k.a. q) of the zero truncated
### negative binomial.
###
### AUTHOR: Vincent Goulet <vincent.goulet@act.ulaval.ca>

dlogarithmic <- function(x, prob, log = FALSE)
    .External(C_actuar_do_dpq, "dlogarithmic", x, prob, log)

plogarithmic <- function(q, prob, lower.tail = TRUE, log.p = FALSE)
    .External(C_actuar_do_dpq, "plogarithmic", q, prob, lower.tail, log.p)

qlogarithmic <- function(p, prob, lower.tail = TRUE, log.p = FALSE)
    .External(C_actuar_do_dpq, "qlogarithmic", p, prob, lower.tail, log.p)

rlogarithmic <- function(n, prob)
    .External(C_actuar_do_random, "rlogarithmic", n, prob)

## not exported; for internal use in panjer()
pgflogarithmic <- function(x, prob)
    log1p(-prob * x)/log1p(-prob)