scModels (version 1.0.4)

Poisson-beta: Poisson-beta Distribution

Description

Density, distribution function, quantile function and random generation for the Poisson-beta distribution: a Poisson distribution whose parameter itself follows a beta distribution. Alpha and beta are the parameters of this specific beta distribution which is scaled on (0, c) in contrast to the usual scaling of the standard beta distribution on (0,1).

Usage

dpb(x, alpha, beta, c = 1, log = FALSE)
ppb(q, alpha, beta, c = 1, lower.tail = TRUE, log.p = FALSE)
qpb(p, alpha, beta, c = 1, lower.tail = TRUE, log.p = FALSE)
rpb(n, alpha, beta, c = 1)

Arguments

x, q

Vector of (non-negative integer) quantiles

alpha, beta

Non-negative parameters of the beta distribution (shape1 and shape2)

c

Numeric scaling parameter of the beta distribution. The standard beta is scaled on (0,1) (default) and can be transformed to (0,c).

log, log.p

Logical; if TRUE, probabilities p are given as log(p)

lower.tail

Logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).

p

Vector of probabilities

n

Number of observations

Examples

 X <- dpb(x=0:200, alpha=5, beta=3, c=20)
 plot(0:200, X, type='l')
 Y <- dpb(0:10, seq(10.0,11.0,by=0.1), seq(30.0,31.0,by=0.1), seq(10.2,11.2,by=0.1))
 Y <- ppb(q= 0 :200, alpha=5, beta= 3, c=20)
 plot(0:200, Y, type="l")
 Z <- qpb(p= seq(0,1, by= 0.01), alpha=5, beta= 3, c=20)
 plot(seq(0,1, by= 0.01),Z, type="l")
 RV <- rpb(n = 1000, alpha=5, beta= 3, c=20)
 plot(0 : 200, X, type="l")
 lines(density(RV), col="red")
 R2 <- rpb(11, seq(10.0,11.0,by=0.1), seq(30.0,31.0,by=0.1), seq(10.2,11.2,by=0.1))