dEOFNH | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Extended Odd Fr?chet-Nadarajah-Haghighi distribution
with parameters mu
, sigma
, nu
and tau
.
dEOFNH(x, mu, sigma, nu, tau, log = FALSE) pEOFNH(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE) qEOFNH(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE) rEOFNH(n, mu, sigma, nu, tau) hEOFNH(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. |
Tthe Extended Odd Frechet-Nadarajah-Haghighi mu
,
sigma
, nu
and tau
has density given by
f(x)= \frac{μσντ(1+ν x)^{σ-1}e^{(1-(1+ν x)^σ)}[1-(1-e^{(1-(1+ν x)^σ)})^{μ}]^{τ-1}}{(1-e^{(1-(1+ν x)^{σ})})^{μτ+1}} e^{-[(1-e^{(1-(1+ν x)^σ)})^{-μ}-1]^{τ}},
for x > 0, μ > 0, σ > 0, ν > 0 and τ > 0.
dEOFNH
gives the density, pEOFNH
gives the distribution
function, qEOFNH
gives the quantile function, rEOFNH
generates random numbers and hEOFNH
gives the hazard function.
Helber Santiago Padilla
nasiru2018extendedRelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ##The probability density function par(mfrow=c(1,1)) curve(dEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from=0, to=10, ylim=c(0, 0.25), col="red", las=1, ylab="f(x)") ## The cumulative distribution and the Reliability function par(mfrow = c(1, 2)) curve(pEOFNH(x,mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from = 0, to = 10, ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)") curve(pEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1, lower.tail = FALSE), from = 0, to = 10, ylim = c(0, 1), col = "red", las = 1, ylab = "R(x)") ##The quantile function p <- seq(from=0, to=0.99999, length.out=100) plot(x=qEOFNH(p, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), y=p, xlab="Quantile", las=1, ylab="Probability") curve(pEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from=0, add=TRUE, col="red") ##The random function hist(rEOFNH(n=10000, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), freq=FALSE, xlab="x", las=1, main="") curve(dEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from=0, add=TRUE, col="red", ylim=c(0,1.25)) ##The Hazard function par(mfrow=c(1,1)) curve(hEOFNH(x, mu=18.5, sigma=5.1, nu=0.1, tau=0.1), from=0, to=10, ylim=c(0, 1), col="red", ylab="Hazard function", las=1) par(old_par) # restore previous graphical parameters
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