NeuDist (version 1.0.1)

InvEEP: Inverse Exponentiated Exponential Poisson (IEEP) Distribution

Description

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

Usage

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

Value

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

• pinv.expo.exp.pois: numeric vector of probabilities

• qinv.expo.exp.pois: numeric vector of quantiles

• rinv.expo.exp.pois: numeric vector of random variates

• hinv.expo.exp.pois: 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 Inverse Exponentiated Exponential Poisson distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Inverse Exponentiated Exponential Poisson distribution has CDF:

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

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

The implementation includes the following functions:

• dinv.expo.exp.pois() — Density function

• pinv.expo.exp.pois() — Distribution function

• qinv.expo.exp.pois() — Quantile function

• rinv.expo.exp.pois() — Random generation

• hinv.expo.exp.pois() — Hazard function

References

Ristic, M.M., & Nadarajah, S.(2014). A New Lifetime Distribution. Journal of Statistical Computation and Simulation, 84(1), 135--150. tools:::Rd_expr_doi("10.1080/00949655.2012.697163")

Telee, L. B. S., & Kumar, V. (2023). Inverse Exponentiated Exponential Poisson Distribution with Theory and Applications. International Journal of Engineering Science Technologies, 7(5), 17--36. tools:::Rd_expr_doi("10.29121/IJOEST.v7.i5.2023.535")

Examples

x <- seq(0.1, 1, 0.1)
dinv.expo.exp.pois(x, 1.5, 0.8, 2)
pinv.expo.exp.pois(x, 1.5, 0.8, 2)
qinv.expo.exp.pois(0.5, 1.5, 0.8, 2)
rinv.expo.exp.pois(10, 1.5, 0.8, 2)
hinv.expo.exp.pois(x, 1.5, 0.8, 2)

#Data
x <- conductors
#ML Estimates    
params = list(alpha =40.5895, beta=22.7519, lambda=2.9979)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pinv.expo.exp.pois, fit.line=TRUE)

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

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