tpmd {new.dist}

Power Muth Distribution

Description

Density, distribution function, quantile function and random generation for the Power Muth distribution with parameters shape and scale.

Usage

dtpmd(x, beta = 1, alpha, log = FALSE)

ptpmd(q, beta = 1, alpha, lower.tail = TRUE, log.p = FALSE)

qtpmd(p, beta = 1, alpha, lower.tail = TRUE)

rtpmd(n, beta = 1, alpha)

Arguments

x, q

vector of quantiles.

beta

a scale parameter.

alpha

a shape 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 Power Muth distribution with shape parameter \alpha and scale parameter \beta has density

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

where

x>0,~\alpha ,\beta>0.

Value

dtpmd gives the density, ptpmd gives the distribution function, qtpmd gives the quantile function and rtpmd generates random deviates.

Note

Hazard function;

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

References

Jodra, P., Gomez, H. W., Jimenez-Gamero, M. D., & Alba-Fernandez, M. V. (2017). The power Muth distribution . Mathematical Modelling and Analysis, 22(2), 186-201.

Examples

library(new.dist)
dtpmd(1, beta=2, alpha=3)
ptpmd(1,beta=2,alpha=3)
qtpmd(.5,beta=2,alpha=3)
rtpmd(10,beta=2,alpha=3)