SB {gentransmuted}R Documentation

The Shaw and Buckley (transmuted) distribution

Description

Density, distribution function, quantile function and random generation for the Shaw and Buckley (SB) distribution.

Usage

dSB(x, lambda = 0, log = FALSE)
pSB(q, lambda = 0, lower.tail = TRUE, log.p = FALSE)
qSB(p, lambda = 0, lower.tail = TRUE, log.p = FALSE)
rSB(n, lambda = 0)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

lambda

shape parameter (by default is 0).

log, log.p

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

lower.tail

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

Details

The SB model has cumulative distribution function

F(x;\delta)=\delta x^2+(1-\delta)[1-(1-x)^2], \quad x \in (0,1),

where \delta=(1-\lambda)/2 and \lambda \in (-1,1).

Value

dSB gives the density, pSB gives the distribution function, qSB gives the quantile function, and rSB generates random deviates. The length of the result is determined by n for rcompound, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

Author(s)

Yolanda M. Gomez, Diego I. Gallardo, Hector W. Gomez and Barry Arnold

Examples

set.seed(2100)
y=rSB(100, lambda = 0.7)

[Package gentransmuted version 1.0 Index]