Description Usage Arguments Details Value Examples
Density, distribution function, quantile function,
random generation and hazard function for the power Lindley distribution with
parameters alpha
and beta
.
1 2 3 4 5 6 7 8 9 |
x,q |
vector of quantiles. |
alpha |
shape parameter. |
beta |
scale 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. |
The power Lindley distribution with parameters alpha
and
beta
has density given by
f(x) = ((alpha*beta^2)/(beta+1))*(1+x^(alpha))*x^(alpha-1)*exp(-beta*(x^alpha))
for x > 0.
dPL
gives the density, pPL
gives the distribution
function, qPL
gives the quantile function, rPL
generates random deviates and hPL
gives the hazard function.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ## The probability density function
curve(dPL(x, alpha = 1, beta = 0.5), from = 0, to = 15, ylim = c(0, 0.25), col = "red", las = 1, ylab = "The probability density function")
## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pPL(x, alpha = 1, beta = 0.5), from = 0, to = 15, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pPL(x, alpha = 1, beta = 0.5, lower.tail = FALSE), from = 0, to = 15, ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")
## The quantile function
p <- seq(from = 0, to = 0.998, length.out = 100)
plot(x=qPL(p=p, alpha = 1, beta = 0.5), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pPL(x, alpha = 1, beta = 0.5), from = 0, add = TRUE, col = "red")
## The random function
hist(rPL(n = 1000, alpha = 1, beta = 0.5), freq = FALSE, , ylim = c(0, 0.25), xlab = "x", las = 1, main = "")
curve(dPL(x, alpha = 1, beta = 0.5), from = 0, add = T, col = "red", ylim = c(0, 0.25))
## The Hazard function
curve(hPL(x, alpha = 1, beta = 0.5), from = 0, to = 10, ylim = c(0, 0.5), col = "red", las = 1, ylab = "The Hazard function")
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