longevity (version 1.2.1)

pbeardmake: Distribution function of the Beard-Makeham distribution

Description

Distribution function of the Beard-Makeham distribution

Density function of the Beard-Makeham distribution

Hazard function of the Beard-Makeham distribution

Quantile function of the Beard-Makeham distribution

Usage

pbeardmake(
  q,
  rate = 1,
  shape1 = 1,
  shape2 = 1,
  lambda = 0,
  lower.tail = TRUE,
  log.p = FALSE
)
dbeardmake(x, rate = rate, shape1 = 1, shape2 = 1, lambda = 0, log = FALSE)
hbeardmake(x, rate = rate, shape1 = 1, shape2 = 1, lambda = 0, log = FALSE)
qbeardmake(p, rate = 1, shape1 = 1, shape2 = 1, lambda = 0, lower.tail = TRUE)

Value

a vector of (log)-probabilities of the same length as q

a vector of (log)-density.

a vector of (log)-hazard.

a vector of quantiles

Arguments

q

vector of quantiles.

rate

shape parameter (\(\nu\))

shape1

shape parameter (\(\alpha\))

shape2

shape parameter (\(\beta\))

lambda

exponential rate of the Makeham component

lower.tail

logical; if TRUE (default), the lower tail probability \(\Pr(X \leq x)\) is returned.

log.p

logical; if FALSE (default), values are returned on the probability scale.

x

vector of quantiles.

log

logical; if FALSE (default), return the hazard

p

vector of probabilities.