NeuDist (version 1.0.1)

ExpoInvChen: Exponentiated Inverse Chen Distribution

Description

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

Usage

dexpo.inv.chen(x, alpha, lambda, theta, log = FALSE)
pexpo.inv.chen(q, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
qexpo.inv.chen(p, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
rexpo.inv.chen(n, alpha, lambda, theta)
hexpo.inv.chen(x, alpha, lambda, theta)

Value

• dexpo.inv.chen: numeric vector of (log-)densities

• pexpo.inv.chen: numeric vector of probabilities

• qexpo.inv.chen: numeric vector of quantiles

• rexpo.inv.chen: numeric vector of random variates

• hexpo.inv.chen: 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 Exponentiated Inverse Chen distribution is parameterized by the parameters \(\alpha > 0\), \(\lambda > 0\), and \(\theta > 0\).

The Exponentiated Inverse Chen distribution has CDF:

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

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

The functions available are listed below:

• dexpo.inv.chen() — Density function

• pexpo.inv.chen() — Distribution function

• qexpo.inv.chen() — Quantile function

• rexpo.inv.chen() — Random generation

• hexpo.inv.chen() — Hazard function

References

Telee, L. B. S., & Kumar, V. (2023). Exponentiated Inverse Chen distribution: Properties and applications. Journal of Nepalese Management Academia, 1(1), 53--62. tools:::Rd_expr_doi("10.3126/jnma.v1i1.62033")

Srivastava, A.K., & Kumar, V.(2011). Markov Chain Monte Carlo Methods for Bayesian Inference of the Chen Model. International Journal of Computer Information Systems, 2(2), 7--14.

Examples

x <- seq(2, 5, 0.25)
dexpo.inv.chen(x, 0.5, 2.5, 1.5)
pexpo.inv.chen(x, 0.5, 2.5, 1.5)
qexpo.inv.chen(0.5, 0.5, 2.5, 1.5)
rexpo.inv.chen(10, 0.5, 2.5, 1.5)
hexpo.inv.chen(x, 0.5, 2.5, 1.5)

# Data
x <- headneck44
# ML estimates
params = list(alpha=0.3947, lambda=15.5330, theta=8.1726)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pexpo.inv.chen, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
# Display plot and print numerical summary
gofic(x, params = params,
      dfun = dexpo.inv.chen, pfun=pexpo.inv.chen, plot=TRUE, verbose = TRUE)