NeuDist (version 1.0.1)

LogisInvExp: Logistic Inverse Exponential Distribution

Description

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

Usage

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

Value

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

• plogis.inv.exp: numeric vector of probabilities

• qlogis.inv.exp: numeric vector of quantiles

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

• hlogis.inv.exp: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

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 Inverse Exponential distribution is parameterized by the parameters \(\alpha > 0\) and \(\lambda > 0\).

The Logistic Inverse Exponential distribution has CDF:

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

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

Available functions are:

• dlogis.inv.exp() — Density function

• plogis.inv.exp() — Distribution function

• qlogis.inv.exp() — Quantile function

• rlogis.inv.exp() — Random generation

• hlogis.inv.exp() — Hazard function

References

Chaudhary, A.K., & Kumar, V. (2020). Logistic Inverse Exponential Distribution with Properties and Applications. International Journal of Mathematics Trends and Technology, 66(10), 151--162. tools:::Rd_expr_doi("10.14445/22315373/IJMTT-V66I10P518")

Examples

x <- seq(0.1, 10, 0.5)
dlogis.inv.exp(x, 2.5, 1.5)
plogis.inv.exp(x, 2.5, 1.5)
qlogis.inv.exp(0.5, 2.5, 1.5)
rlogis.inv.exp(10, 2.5, 1.5)
hlogis.inv.exp(x, 2.5, 1.5)

# Data
x <- stress31
# ML estimates
params = list(alpha=7.6230, lambda=91.7136)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = plogis.inv.exp, fit.line=TRUE)

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

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