NeuDist (version 1.0.1)

InvExpPower: Inverse Exponential Power Distribution

Description

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

Usage

dinv.exp.power(x, alpha, lambda, log = FALSE)
pinv.exp.power(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qinv.exp.power(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rinv.exp.power(n, alpha, lambda)
hinv.exp.power(x, alpha, lambda)

Value

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

• pinv.exp.power: numeric vector of probabilities

• qinv.exp.power: numeric vector of quantiles

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

• hinv.exp.power: 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 Inverse Exponential Power distribution is parameterized by the parameters \(\alpha > 0\) and \(\lambda > 0\).

The Inverse Exponential Power distribution has CDF:

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

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

The implementation includes the following functions:

• dinv.exp.power() — Density function

• pinv.exp.power() — Distribution function

• qinv.exp.power() — Quantile function

• rinv.exp.power() — Random generation

• hinv.exp.power() — Hazard function

References

Chaudhary, A.K., Sapkota,L.P. & Kumar, V.(2023). Inverse Exponential Power distribution: Theory and Applications. International Journal of Mathematics, Statistics and Operations Research, 3(1), 175--185.

Examples

x <- seq(1.0, 5.0, 0.2)
dinv.exp.power(x, 2.5, 0.5)
pinv.exp.power(x, 2.5, 0.5)
qinv.exp.power(0.5, 2.5, 0.5)
rinv.exp.power(10, 2.5, 0.5)
hinv.exp.power(x, 2.5, 0.5)

# Data
x <- relief
# ML estimates
params = list(alpha=2.8286, lambda=1.3346)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pinv.exp.power, fit.line=TRUE)

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

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