NeuDist (version 1.0.1)

ModGE: Modified Generalized Exponential (MGE) Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Modified Generalized Exponential distribution.

Usage

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

Value

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

• pmod.gen.exp: numeric vector of probabilities

• qmod.gen.exp: numeric vector of quantiles

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

• hmod.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 Modified Generalized Exponential distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Modified Generalized Exponential distribution has CDF:

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

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

The following functions are included:

• dmod.gen.exp() — Density function

• pmod.gen.exp() — Distribution function

• qmod.gen.exp() — Quantile function

• rmod.gen.exp() — Random generation

• hmod.gen.exp() — Hazard function

References

Telee, L. B. S., & Kumar, V. (2023). Modified Generalized Exponential Distribution. Nepal Journal ofMathematical Sciences, 4(1), 21–32. tools:::Rd_expr_doi("10.3126/njmathsci.v4i1.53154")

Chaudhary, A. K., Sapkota, L. P., & Kumar, V.(2021). Some Properties and Application of Arctan Generalized Exponential Distribution. International Journal of Innovative Research in Science, Engineering and Technology (IJIRSET), 10(1),456--468.

Examples

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

# Data
x <- stress  
# ML estimates
params = list(alpha=3.1502, beta=0.2167, lambda=0.3636)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pmod.gen.exp, fit.line=TRUE)

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

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