NeuDist (version 1.0.1)

LogisExpPower: Logistic-Exponential Power (LEP) Distribution

Description

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

Usage

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

Value

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

• plogis.exp.power: numeric vector of probabilities

• qlogis.exp.power: numeric vector of quantiles

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

• hlogis.exp.power: 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 Power distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Logistic-Exponential Power distribution has CDF:

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

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

The implementation includes the following functions:

• dlogis.exp.power() — Density function

• plogis.exp.power() — Distribution function

• qlogis.exp.power() — Quantile function

• rlogis.exp.power() — Random generation

• hlogis.exp.power() — Hazard function

References

Joshi, R. K., Sapkota, L.P., & Kumar, V. (2020). The Logistic-Exponential Power Distribution with Statistical Properties and Applications. International Journal of Emerging Technologies and Innovative Research, 7(12), 629--641.

Examples

x <- seq(0.1, 2.0, 0.1)
dlogis.exp.power(x, 1.5, 1.5, 0.1)
plogis.exp.power(x, 1.5, 1.5, 0.1)
qlogis.exp.power(0.5, 1.5, 1.5, 0.1)
rlogis.exp.power(10, 2.0, 5.0, 0.1)
hlogis.exp.power(x, 1.5, 1.5, 0.1)

# Data
x <- stress
# ML estimates
params = list(alpha=1.8940, beta=1.2276, lambda=0.1650)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.exp.power, fit.line=TRUE)

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

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