MO {gentransmuted}R Documentation

The Marshall-Olkin and Marshall-Olkin of the second kind distributions

Description

Density, distribution function, quantile function and random generation for the Marshall-Olkin (MO) and Marshall-Olkin of the second kind (MO2) distributions.

Usage

dMO(x, theta = 1, log = FALSE)
pMO(q, theta = 1, lower.tail = TRUE, log.p = FALSE)
qMO(p, theta = 1, lower.tail = TRUE, log.p = FALSE)
rMO(n, theta = 1)
dMO2(x, theta = 1, log = FALSE)
pMO2(q, theta = 1, lower.tail = TRUE, log.p = FALSE)
qMO2(p, theta = 1, lower.tail = TRUE, log.p = FALSE)
rMO2(n, theta = 1)

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.

theta

shape parameter (by default is 1).

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 MO model has cumulative distribution function

F(x;\alpha)=\frac{\theta x}{1-(1-\theta)x}, \quad x \in (0,1), \theta>0,

whereas the MO2 model has cumulative distribution function

F(x;\alpha)=\frac{x}{1-(1-\theta)(1-x)}, \quad x \in (0,1), \alpha>0,

Value

dEXP and dEXP2 give the density, pEXP and pEXP2 give the distribution function, qEXP and qEXP2 give the quantile function, and rEXP and rEXP2 generate 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=rMO(100, theta = 1.2)

[Package gentransmuted version 1.0 Index]