dRNMW: The New Modified Weibull distribution

In ousuga/RelDists: Estimation for some Reliability Distributions

The New Modified Weibull distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the reduced new modified Weibull distribution with parameters mu, sigma and nu.

Usage

dRNMW(x, mu, sigma, nu, log = FALSE)

Arguments

x, q	vector of quantiles.
mu	parameter one.
sigma	parameter two.
nu	parameter three.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
p	vector of probabilities.
n	number of observations.
lower.tail	logical; if TRUE (default), probabilities are P[T <= t], otherwise, P[T > t].

Details

The reduced new modified Weibull with parameters mu, sigma and theta has density given by

f(x) = \frac{1}{2 \sqrt{x}} \left( \mu + \sigma (1 + 2 \nu x) e^{\nu x} \right) e^{-\mu \sqrt{x} - \sigma \sqrt{x} e^{\nu x}}

for x > 0,

\mu

,

\sigma

and

\lambda

> 0.

Value

dRNMW gives the density, pRNMW gives the distribution function, qRNMW gives the quantile function, rRNMW generates random deviates and hRNMW gives the hazard function.

References

\insertRef

almalki2013reducedRelDists

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function
curve(
    dRNMW(x, mu = 0.05, sigma = 0.00025, nu = 2.2),
    from = 0, to = 5, col = "red", las = 1, ylab = "f(x)"
)

## The cualphalative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(
    pRNMW(x, mu = 0.05, sigma = 0.00025, nu = 2.2),
    from = 0, to = 5, ylim = c(0, 1),
    col = "red", las = 1, ylab = "F(x)"
)
curve(
    pRNMW(
        x, mu = 0.05, sigma = 0.00025, nu = 2.2, 
        lower.tail = FALSE
    ),
    from = 0, to = 5, ylim = c(0, 1),
    col = "red", las = 1, ylab = "R(x)"
)

## The quantile function
p <- seq(from = 0, to = 0.999, length.out = 100)
plot(
    x = qRNMW(p, mu = 0.05, sigma = 0.00025, nu = 2.2),
    y = p, xlab = "Quantile", las = 1,
    ylab = "Probability"
)
curve(
    pRNMW(x, mu = 0.05, sigma = 0.00025, nu = 2.2),
    from = 0, add = TRUE, col = "red"
)

## The random function
hist(
    rRNMW(n = 10000, mu = 0.05, sigma = 0.00025, nu = 2.2),
    freq = FALSE, xlab = "x", las = 1, main = "", ylim = c(0,0.8)
)
curve(dRNMW(x, mu = 0.05, sigma = 0.00025, nu = 2.2),
    from = 0, add = TRUE, col = "red"
)

## The Hazard function
par(mfrow = c(1, 1))
curve(
    hRNMW(x, mu = 0.003, sigma = 5e-6, nu = 0.025),
    from = 0, to = 250, col = "red", 
    ylab = "Hazard function", las = 1
)

par(old_par) # restore previous graphical parameters

ousuga/RelDists documentation built on Feb. 16, 2025, 5:22 p.m.