PoissonChen: Poisson-Chen Distribution

Description

Provides density, distribution, quantile, random generation, and hazard functions for the Poisson-Chen distribution.

Usage

dpois.chen(x, alpha, beta, lambda, log = FALSE)
ppois.chen(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
qpois.chen(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)
rpois.chen(n, alpha, beta, lambda)
hpois.chen(x, alpha, beta, lambda)

Value

dpois.chen: numeric vector of (log-)densities
ppois.chen: numeric vector of probabilities
qpois.chen: numeric vector of quantiles
rpois.chen: numeric vector of random variates
hpois.chen: 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 Poisson-Chen distribution is parameterized by the parameters $\alpha > 0$, $\beta > 0$, and $\lambda > 0$.

The Poisson-Chen distribution has CDF:

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

where $\alpha$, $\beta$, and $\lambda$ are the parameters.

The following functions are included:

dpois.chen() — Density function
ppois.chen() — Distribution function
qpois.chen() — Quantile function
rpois.chen() — Random generation
hpois.chen() — Hazard function

References

Joshi, R. K., & Kumar, V. (2021). Poisson Chen Distribution: Properties and Application. International Journal of Latest Trends in Engineering and Technology, 18(4), 1--12.

Examples

Run this code

x <- seq(0.1, 2.0, 0.2)
dpois.chen(x, 2.0, 0.5, 0.2)
ppois.chen(x, 2.0, 0.5, 0.2)
qpois.chen(0.5, 2.0, 0.5, 0.2)
rpois.chen(10, 2.0, 0.5, 0.2)
hpois.chen(x, 2.0, 0.5, 0.2)

# Data
x <- fibers63
# ML estimates
params = list(alpha=0.53679, beta=1.00238, lambda=108.22948)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = ppois.chen, fit.line=TRUE)

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

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dpois.chen, pfun=ppois.chen, plot=TRUE)
print.gofic(out)

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