omd {new.dist}

Muth Distribution

Description

Density, distribution function, quantile function and random generation for on the Muth distribution.

Usage

domd(x, alpha, log = FALSE)

pomd(q, alpha, lower.tail = TRUE, log.p = FALSE)

qomd(p, alpha, lower.tail = TRUE)

romd(n, alpha)

Arguments

x, q

vector of quantiles.

alpha

a parameter.

log, log.p

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

lower.tail

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

p

vector of probabilities.

n

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

Details

The Muth distribution with a parameter \alpha, has density

f\left( x\right) =\left( e^{\alpha x}- \alpha \right) e^{\alpha x-\left(1/\alpha \right) \left( e^{\alpha x}- 1\right) },

where

x>0,~\alpha \in \left( 0,1\right].

Value

domd gives the density, pomd gives the distribution function, qomd gives the quantile function and romd generates random deviates.

References

Jodrá, P., Jiménez-Gamero, M. D. ve Alba-Fernández, M. V., 2015, On the Muth distribution, Mathematical Modelling and Analysis, 20 (3), 291-310.

Examples

library(new.dist)
domd(1,alpha=.2)
pomd(1,alpha=.2)
qomd(.8,alpha=.1)
romd(10,alpha=1)