Description Usage Arguments Details Value Examples
Density, distribution function, quantile function,
random generation and hazard function for the weibull geometric distribution with
parameters alpha
, beta
and pi
.
1 2 3 4 5 6 7 8 9 |
x,q |
vector of quantiles. |
alpha |
shape parameter. |
beta |
scale parameter. |
pi |
parameter of geometric random variable. |
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 weibull geometric distribution with parameters alpha
,
beta
and pi
has density given by
f(x) = (alpha*(beta)^alpha*(1-pi)*x^(alpha-1)*exp(-(beta*x)^alpha))/(1- pi*exp(-(beta*x)^alpha))^2
for x > 0.
dWG
gives the density, pWG
gives the distribution
function, qWG
gives the quantile function, rWG
generates random deviates and hWG
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(dWG(x, alpha = 0.5, beta = 0.2, pi = 0.95), from = 0, to = 5, ylim = c(0, 1.5), col = "red", las = 1, ylab = "The probability density function")
## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pWG(x, alpha = 0.5, beta = 0.2, pi = 0.95), from = 0, to = 5, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pWG(x, alpha = 0.5, beta = 0.2, pi = 0.95, lower.tail = FALSE), from = 0, to = 5, ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")
## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qWG(p = p, alpha = 0.5, beta = 0.2, pi = 0.95), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pWG(x, alpha = 0.5, beta = 0.2, pi = 0.95), from = 0, add = TRUE, col = "red")
## The random function
hist(rWG(1000, alpha = 0.5, beta = 0.2, pi = 0.95), freq = FALSE, xlab = "x", ylim = c(0, 0.2), las = 1, main = "")
curve(dWG(x, alpha = 0.5, beta = 0.2, pi = 0.95), from = 0, add = TRUE, col = "red", ylim = c(0, 0.2))
## The Hazard function
curve(hWG(x, alpha = 0.5, beta = 0.2, pi = 0.95), from = 0, to = 15, ylim = c(0, 2.2), col = "red", ylab = "The hazard function", las = 1)
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