NeuDist (version 1.0.1)

ExpoExpPower: Exponentiated Exponential Power (EEP) Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Exponentiated Exponential Power (EEP) distribution.

Usage

dgen.exp.power(x, alpha, lambda, theta, log = FALSE)
pgen.exp.power(q, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
qgen.exp.power(p, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
rgen.exp.power(n, alpha, lambda, theta)
hgen.exp.power(x, alpha, lambda, theta)

Value

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

• pgen.exp.power: numeric vector of probabilities

• qgen.exp.power: numeric vector of quantiles

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

• hgen.exp.power: numeric vector of hazard values

Arguments

x, q

numeric vector of quantiles (x, q)

alpha

positive numeric parameter

lambda

positive numeric parameter

theta

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 EEP distribution is parameterized by the parameters \(\alpha > 0\), \(\lambda > 0\), and \(\theta > 0\).

The Exponentiated Exponential Power (EEP) distribution has CDF:

$$ F(x;\,\alpha ,\;\lambda ,\theta ) = {\left[ {1 - \exp \left\{ {1 - \exp \left( {\lambda {x^\alpha }} \right)} \right\}} \right]^\theta }\;\;\;;\;\;x > 0 $$

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

The implementation includes the following functions:

• dgen.exp.power() — Density function

• pgen.exp.power() — Distribution function

• qgen.exp.power() — Quantile function

• rgen.exp.power() — Random generation

• hgen.exp.power() — Hazard function

References

Sapkota, L.P., & Kumar, V.(2024). Bayesian Analysis of Exponentiated Exponential Power Distribution under Hamiltonian Monte Carlo Method, Statistics and Applications. Statistics and Applications, 22(2), 231--258.

Srivastava, A.K., & Kumar, V.(2011). Analysis of Software Reliability Data using Exponential Power Model. International Journal of Advanced Computer Science and Applications, 2(2), 38--45, tools:::Rd_expr_doi("10.14569/IJACSA.2011.020208")

Chen, Z.(1999). Statistical inference about the shape parameter of the exponential power distribution, Statistical Papers, 40, 459--468.

Smith, R.M., & Bain, L.J. (1975). An exponential power life-test distribution. IEEE Communications in Statistics, 4, 469--481.

Examples

x <- seq(0.1, 1, 0.1)
dgen.exp.power(x, 1.5, 0.8, 2)
pgen.exp.power(x, 1.5, 0.8, 2)
qgen.exp.power(0.5, 1.5, 0.8, 2)
rgen.exp.power(10, 1.5, 0.8, 2)
hgen.exp.power(x, 1.5, 0.8, 2)
#Data
x <- waiting
#ML Estimates    
params = list(alpha=0.3407, lambda=0.6068, theta=7.6150)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pgen.exp.power, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
# Neither plot nor console output; results stored in 'out'
out <- gofic(x, params = params,
             dfun = dgen.exp.power, pfun = pgen.exp.power, plot=FALSE)
print.gofic(out)