The Reduced New Modified Weibull distribution

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)

pRNMW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qRNMW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

rRNMW(n, mu, sigma, nu)

hRNMW(x, mu, sigma, nu)

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).
lower.tail: logical; if TRUE (default), probabilities are P[T <= t], otherwise, P[T > t].
p: vector of probabilities.
n: number of observations.

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.

Details

The reduced new modified Weibull with parameters mu, sigma and nu 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 $x > 0$, $\mu>0$, $\sigma>0$ and $\nu>0$.

References

Almalki, S. J. (2018). A reduced new modified Weibull distribution. Communications in Statistics-Theory and Methods, 47(10), 2297-2313.

Author

Jaime Mosquera, jmosquerag@unal.edu.co

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