Description Usage Arguments Details Value Examples
Density, distribution function, quantile function, random generation and hazard function for the generalized
modified weibull distribution with parameters beta
, theta
, gamma
and lambda
.
1 2 3 4 5 6 7 8 9 |
beta |
parameter one. |
theta |
parameter two. |
gamma |
parameter three. |
lambda |
parameter four. |
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. |
x,q |
vector of quantiles. |
The generalized modified weibull with parameters beta
, theta
,
gamma
and lambda
has density given by
f(x)= beta*theta*x^(gamma-1)*(gamma+lambda*x)*exp(lambda*x-beta*x^(gamma)*exp(lambda*x))* (1-exp(beta*x^(gamma)*exp(lambda*x)))^(theta-1)
for x>0.
#'
dGMW
gives the density, pGMW
gives the distribution
function, qGMW
gives the quantile function, rGMW
generates random deviates and hGMW
gives the hazard function.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ## The probability density function
curve(dGMW(x, beta = 2, theta = 0.5, gamma = 2, lambda = 1.5), from = 0, to = 0.8, ylim = c(0, 6), col = "red", las = 1, ylab = "The probability density function")
## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pGMW(x, beta = 2, theta = 0.5, gamma = 2, lambda = 1.5), from = 0, to = 1.2, col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pGMW(x, beta = 2, theta = 0.5, gamma = 2, lambda = 1.5, lower.tail = FALSE), from = 0, to = 1.2, col = "red", las = 1, ylab = "The Reliability function")
## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qGMW(p, beta = 2, theta = 0.5, gamma = 2, lambda = 0.3), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pGMW(x, beta = 2, theta = 0.5, gamma = 2, lambda = 0.3), from = 0, add = TRUE, col="red")
## The random function
hist(rGMW(n = 1000, beta = 2, theta = 0.5, gamma = 2,lambda = 0.3), freq = FALSE, xlab = "x", main ="", las = 1)
curve(dGMW(x, beta = 2, theta = 0.5, gamma = 2, lambda = 0.3), from = 0, add = TRUE, col = "red")
## The Hazard function
curve(hGMW(x, beta = 2, theta = 1.5, gamma = 2, lambda = 0.8), from = 0, to = 1, ylim = c(0, 16), col = "red", ylab = "The Hazard function", las = 1)
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