dPL: The Power Lindley distribution

In ousuga/RelDists: Estimation for some Reliability Distributions

The Power Lindley distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the Power Lindley distribution with parameters mu and sigma.

Usage

dPL(x, mu, sigma, log = FALSE)

pPL(q, mu, sigma, lower.tail = TRUE, log.p = FALSE)

qPL(p, mu, sigma, lower.tail = TRUE, log.p = FALSE)

rPL(n, mu, sigma)

hPL(x, mu, sigma)

Arguments

x, q	vector of quantiles.
mu	parameter.
sigma	parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
p	vector of probabilities.
n	number of observations.

Details

The Power Lindley Distribution with parameters mu and sigma has density given by

f(x) = \frac{μ σ^2}{σ + 1} (1 + x^μ) x ^ {μ - 1} \exp({-σ x ^μ}),

for x > 0.

Value

dPL gives the density, pPL gives the distribution function, qPL gives the quantile function, rPL generates random deviates and hPL gives the hazard function.

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

Ghitanya2013RelDists

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function
curve(dPL(x, mu=1.5, sigma=0.2), from=0.1, to=10,
      col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pPL(x, mu=1.5, sigma=0.2),
      from=0.1, to=10, col="red", las=1, ylab="F(x)")
curve(pPL(x, mu=1.5, sigma=0.2, lower.tail=FALSE),
      from=0.1, to=10, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qPL(p, mu=1.5, sigma=0.2), y=p, xlab="Quantile",
     las=1, ylab="Probability")
curve(pPL(x, mu=1.5, sigma=0.2), from=0.1, add=TRUE, col="red")

## The random function
hist(rPL(n=1000, mu=1.5, sigma=0.2), freq=FALSE,
     xlab="x", las=1, main="")
curve(dPL(x, mu=1.5, sigma=0.2), from=0.1, to=15, add=TRUE, col="red")

## The Hazard function
par(mfrow=c(1,1))
curve(hPL(x, mu=1.5, sigma=0.2), from=0.1, to=15,
      col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters

ousuga/RelDists documentation built on Jan. 12, 2023, 10:27 p.m.