NeuDist (version 1.0.1)

ModInvGE: Modified Inverse Generalized Exponential(MIGE) Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the MIGE distribution.

Usage

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

Value

• dmod.inv.gen.exp: numeric vector of (log-)densities

• pmod.inv.gen.exp: numeric vector of probabilities

• qmod.inv.gen.exp: numeric vector of quantiles

• rmod.inv.gen.exp: numeric vector of random variates

• hmod.inv.gen.exp: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

positive numeric parameter

beta

positive numeric parameter

lambda

positive numeric parameter

log

logical; if TRUE, returns log-density

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).

log.p

logical; if TRUE, probabilities are given as log(p)

p

numeric vector of probabilities (0 < p < 1)

n

number of observations (integer > 0)

Details

The MIGE distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Modified Inverse Generalized Exponential(MIGE) distribution has CDF:

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

where \(\alpha\), \(\beta\), and \(\lambda\) are the parameters.

The following functions are included:

• dmod.inv.gen.exp() — Density function

• pmod.inv.gen.exp() — Distribution function

• qmod.inv.gen.exp() — Quantile function

• rmod.inv.gen.exp() — Random generation

• hmod.inv.gen.exp() — Hazard function

References

Krishna, H., & Kumar, K. (2013). Reliability estimation in generalized inverted exponential distribution with progressive type II censored sample. Journal of Statistical Computation and Simulation, 83(6), 1007--1019.

Telee, L. B. S., & Kumar, V. (2023). Modified Inverse Generalized Exponential Distribution : Model and Properties. Int. J. Res. Granthaalayah, 11(8), 96--111. tools:::Rd_expr_doi("10.29121/granthaalayah.v11.i8.2023.5288")

Examples

x <- seq(0.1, 10, 0.2)
dmod.inv.gen.exp(x, 2.0, 0.5, 0.2)
pmod.inv.gen.exp(x, 2.0, 0.5, 0.2)
qmod.inv.gen.exp(0.5, 2.0, 0.5, 0.2)
rmod.inv.gen.exp(10, 2.0, 0.5, 0.2)
hmod.inv.gen.exp(x, 2.0, 0.5, 0.2)

# Data
x <- fibers69
# ML estimates
params = list(alpha=30.7790, beta=0.1942, lambda=14.8297)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pmod.inv.gen.exp, fit.line=TRUE)

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

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