ModInvLomax: Modified Inverse Lomax (MIL) Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Modified Inverse Lomax distribution.

Usage

dmod.inv.lomax(x, alpha, beta, lambda, log = FALSE)
pmod.inv.lomax(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qmod.inv.lomax(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rmod.inv.lomax(n, alpha, beta, lambda)
hmod.inv.lomax(x, alpha, beta, lambda)

Value

dmod.inv.lomax: numeric vector of (log) densities.
pmod.inv.lomax: numeric vector of distribution function values.
qmod.inv.lomax: numeric vector of quantiles.
rmod.inv.lomax: numeric vector of random variates.
hmod.inv.lomax: numeric vector of hazard rates.

Arguments

x: numeric vector of strictly positive quantiles.
alpha: positive shape parameter.
beta: positive scale parameter.
lambda: positive shape/scale parameter.
log: logical; if TRUE, returns the log-density.
q: numeric vector of strictly positive quantiles.
lower.tail: logical; if TRUE (default), probabilities are $P(X \le x)$, otherwise $P(X > x)$.
log.p: logical; if TRUE, probabilities are returned as log(p).
p: numeric vector of probabilities with values in (0, 1).
n: number of observations (positive integer).

Details

The distribution is parameterized by shape parameters $\alpha > 0$, $\beta > 0$ and scale/shape parameter $\lambda > 0$.

The cumulative distribution function (CDF) of the MIL distribution is

$$ F(x; \alpha,\beta,\lambda) = \left[1+\left(\frac{\beta}{x}\right)e^{-\lambda x}\right]^{-\alpha}, \quad x>0. $$

References

Telee, L.B.S., Yadav, R.S., & Kumar V.(2023). Modified Inverse Lomax Distribution: Model and properties. Discovery, 59: e110d1352. tools:::Rd_expr_doi("10.54905/disssi.v59i333.e110d1352")

Examples

Run this code

x <- seq(0.1, 5, by = 0.1)
dmod.inv.lomax(x, alpha = 1.5, beta = 2, lambda = 0.5)
pmod.inv.lomax(x, alpha = 1.5, beta = 2, lambda = 0.5)
qmod.inv.lomax(0.5, alpha = 1.5, beta = 2, lambda = 0.5)
set.seed(123)
rmod.inv.lomax(5, alpha = 1.5, beta = 2, lambda = 0.5)
hmod.inv.lomax(x, alpha = 1.5, beta = 2, lambda = 0.5)

# Data
x <- windshield
# ML estimates
params = list(alpha=0.6661, beta=26.8875, lambda=1.0004)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pmod.inv.lomax, fit.line=TRUE)

#Q-Q (quantile–quantile) plot 
qq.plot(x, params = params, qfun = qmod.inv.lomax, fit.line=TRUE)

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dmod.inv.lomax, pfun=pmod.inv.lomax, plot=FALSE)
print.gofic(out)

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