dMOK | R Documentation |
Desnsity, distribution function, quantile function,
random generation and hazard function for the Marshall-Olkin Kappa distribution
with parameters mu
, sigma
, nu
and tau
.
dMOK(x, mu, sigma, nu, tau, log = FALSE) pMOK(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE) qMOK(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE) rMOK(n, mu, sigma, nu, tau) hMOK(x, mu, sigma, nu, tau)
x, q |
vector of quantiles. |
mu |
parameter. |
sigma |
parameter. |
nu |
parameter. |
tau |
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 Marshall-Olkin Kappa distribution with parameters mu
,
sigma
, nu
and tau
has density given by:
f(x)=\frac{τ\frac{μν}{σ}≤ft(\frac{x}{σ}\right)^{ν-1} ≤ft(μ+≤ft(\frac{x}{σ}\right)^{μν}\right)^{-\frac{μ+1}{μ}}}{≤ft[τ+(1-τ)≤ft(\frac{≤ft(\frac{x}{σ}\right)^{μν}}{μ+≤ft(\frac{x}{σ}\right)^{μν}}\right)^{\frac{1}{μ}}\right]^2}
for x > 0.
dMOK
gives the density, pMOK
gives the distribution function,
qMOK
gives the quantile function, rMOK
generates random deviates
and hMOK
gives the hazard function.
Angel Muñoz,
javed2018marshallRelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function par(mfrow = c(1,1)) curve(dMOK(x = x, mu = 1, sigma = 3.5, nu = 3, tau = 2), from = 0, to = 15, ylab = 'f(x)', col = 2, las = 1) ## The cumulative distribution and the Reliability function par(mfrow = c(1,2)) curve(pMOK(q = x, mu = 1, sigma = 2.5, nu = 3, tau = 2), from = 0, to = 10, col = 2, lwd = 2, las = 1, ylab = 'F(x)') curve(pMOK(q = x, mu = 1, sigma = 2.5, nu = 3, tau = 2, lower.tail = FALSE), from = 0, to = 10, col = 2, lwd = 2, las = 1, ylab = 'R(x)') ## The quantile function p <- seq(from = 0.00001, to = 0.99999, length.out = 100) plot(x = qMOK(p = p, mu = 4, sigma = 2.5, nu = 3, tau = 2), y = p, xlab = 'Quantile', las = 1, ylab = 'Probability') curve(pMOK(q = x, mu = 4, sigma = 2.5, nu = 3, tau = 2), from = 0, to = 15, add = TRUE, col = 2) ## The random function hist(rMOK(n = 10000, mu = 1, sigma = 2.5, nu = 3, tau = 2), freq = FALSE, xlab = "x", las = 1, main = '', ylim = c(0,.3), xlim = c(0,20), breaks = 50) curve(dMOK(x, mu = 1, sigma = 2.5, nu = 3, tau = 2), from = 0, to = 15, add = TRUE, col = 2) ## The Hazard function par(mfrow = c(1,1)) curve(hMOK(x = x, mu = 1, sigma = 2.5, nu = 3, tau = 2), from = 0, to = 20, col = 2, ylab = 'Hazard function', las = 1) par(old_par) # restore previous graphical parameters
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