dLIN: Lindley distribution

In ousuga/RelDists: Estimation for some Reliability Distributions

Lindley distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the Lindley distribution with parameter mu.

Usage

dLIN(x, mu, log = FALSE)

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

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

rLIN(n, mu)

hLIN(x, mu, log = FALSE)

Arguments

x, q	vector of quantiles.
mu	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

Lindley Distribution with parameter mu has density given by

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

for x > 0 and μ > 0. These function were taken form LindleyR package.

Value

dLIN gives the density, pLIN gives the distribution function, qLIN gives the quantile function, rLIN generates random deviates and hLIN gives the hazard function.

Author(s)

Freddy Hernandez, [e-mail]

References

\insertRef

lindley1958fiducialRelDists

\insertRef

lindley1965introductionRelDists

Examples

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

## The probability density function
curve(dLIN(x, mu=1.5), from=0.0001, to=10,
      col="red", las=1, ylab="f(x)")

## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pLIN(x, mu=2), from=0.0001, to=10, col="red", las=1, ylab="F(x)")
curve(pLIN(x, mu=2, lower.tail=FALSE), from=0.0001, 
      to=10, col="red", las=1, ylab="R(x)")

## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qLIN(p, mu=2), y=p, xlab="Quantile", las=1, ylab="Probability")
curve(pLIN(x, mu=2), from=0, add=TRUE, col="red")

## The random function
hist(rLIN(n=10000, mu=2), freq=FALSE, xlab="x", las=1, main="")
curve(dLIN(x, mu=2), from=0.09, to=5, add=TRUE, col="red")

## The Hazard function
curve(hLIN(x, mu=2), from=0.001, to=10, 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.