Description Usage Arguments Details Value Examples
Density, distribution function, quantile function,
random generation and hazard function for the Almaki and Yuan's modified weibull distribution with
parameters alpha
, beta
, theta
, gamma
and lambda
.
1 2 3 4 5 6 7 8 9 | dNMW(x, alpha, beta, theta, gamma, lambda, log = FALSE)
pNMW(q, alpha, beta, theta, gamma, lambda, lower.tail = TRUE, log.p = FALSE)
qNMW(p, alpha, beta, theta, gamma, lambda, lower.tail = TRUE, log.p = FALSE)
rNMW(n, alpha, beta, theta, gamma, lambda)
hNMW(x, alpha, beta, theta, gamma, lambda, log = FALSE)
|
x,q |
vector of quantiles. |
alpha |
parameter one. |
beta |
parameter two. |
theta |
parameter three. |
gamma |
parameter four. |
lambda |
parameter five. |
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 Almaki and Yuans modified weibull with parameters alpha
,
beta
, theta
, gamma
and lambda
has density given by
f(x)=(alpha*theta*x^(theta-1)+beta*(gamma+ lambda*x)*(x^(gamma-1)*exp(lambda*x)))*(exp((-alpha*x^theta)-(beta*x^gamma*exp(lambda*x)))
for x>0.
dNMW
gives the density, pNMW
gives the distribution
function, qNMW
gives the quantile function, rNMW
generates random deviates and hNMW
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(dNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, to = 1.4, ylim = c(0, 3), col = "red", las = 1, ylab = "The probability density function")
## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, to = 1.4, col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2, lower.tail = FALSE), from = 0, to = 1.4, col = "red", las = 1, ylab = "The Reliability function")
## The quantile function
p <- seq(from = 0, to = 0.998, length.out = 100)
plot(x=qNMW(p, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, add = TRUE, col = "red")
## The random function
hist(rNMW(n = 1000, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), freq = FALSE, ylim = c(0, 3), xlab = "x", las = 1, main = "")
curve(dNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, ylim = c(0, 3), add = T, col = "red")
## The Hazard function
curve(hNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, to = 1.5, ylim = c(0, 8), col = "red", ylab = "The hazard function", las = 1)
|
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