NeuDist (version 1.0.1)

LogisModExp: Logistic Modified Exponential Distribution

Description

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

Usage

dlogis.mod.exp(x, alpha, beta, lambda, log = FALSE)
plogis.mod.exp(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qlogis.mod.exp(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rlogis.mod.exp(n, alpha, beta, lambda)
hlogis.mod.exp(x, alpha, beta, lambda)

Value

• dlogis.mod.exp: numeric vector of (log-)densities

• plogis.mod.exp: numeric vector of probabilities

• qlogis.mod.exp: numeric vector of quantiles

• rlogis.mod.exp: numeric vector of random variates

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

The Logistic Modified Exponential distribution has CDF:

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

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

The following functions are included:

• dlogis.mod.exp() — Density function

• plogis.mod.exp() — Distribution function

• qlogis.mod.exp() — Quantile function

• rlogis.mod.exp() — Random generation

• hlogis.mod.exp() — Hazard function

References

Chaudhary, A.K., & Kumar, V.(2020). A Study on Properties and Applications of Logistic Modified Exponential Distribution. International Journal of Latest Trends In Engineering and Technology (IJLTET),18(1),19--29.

Examples

x <- seq(0.1, 2.0, 0.2)
dlogis.mod.exp(x, 1.5, 1.5, 0.2)
plogis.mod.exp(x, 1.5, 1.5, 0.2)
qlogis.mod.exp(0.5, 1.5, 1.5, 0.2)
rlogis.mod.exp(10, 1.5, 1.5, 0.2)
hlogis.mod.exp(x, 1.5, 1.5, 0.2)

# Data
x <- stress
# ML estimates
params = list(alpha=2.0354, beta=0.1891, lambda=0.1656)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.mod.exp, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dlogis.mod.exp, pfun=plogis.mod.exp, plot=TRUE)
print.gofic(out)