NeuDist (version 1.0.1)

LogisExpExt: Logistic-Exponential Extension Distribution

Description

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

Usage

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

Value

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

• plogis.exp.ext: numeric vector of probabilities

• qlogis.exp.ext: numeric vector of quantiles

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

• hlogis.exp.ext: 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-Exponential Extension distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Logistic-Exponential Extension distribution has CDF:

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

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

The implementation includes the following functions:

• dlogis.exp.ext() — Density function

• plogis.exp.ext() — Distribution function

• qlogis.exp.ext() — Quantile function

• rlogis.exp.ext() — Random generation

• hlogis.exp.ext() — Hazard function

References

Chaudhary,A.K., & Kumar, V.(2020). A Study on Properties and Real Data Applications of the Logistic Exponential Extension Distribution with Properties. International Journal of Latest Trends In Engineering and Technology (IJLTET), 18(2), 20-30.

Examples

x <- seq(0.1, 10, 0.2)
dlogis.exp.ext(x, 2.0, 5.0, 0.1)
plogis.exp.ext(x, 2.0, 5.0, 0.1)
qlogis.exp.ext(0.5, 2.0, 5.0, 0.1)
rlogis.exp.ext(10, 2.0, 5.0, 0.1)
hlogis.exp.ext(x, 2.0, 5.0, 0.1)

# Data
x <- stress31
# ML estimates
params = list(alpha=1.7919, beta=418.0473, lambda=0.1211)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.exp.ext, fit.line=TRUE)

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

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