RelDists (version 1.0.0)

dLIN: 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)

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.

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.

Author

Freddy Hernandez,

Details

Lindley Distribution with parameter mu has density given by

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

for x > 0 and \(\mu > 0\). These function were taken form LindleyR package.

References

lindley1958fiducialRelDists

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