NeuDist (version 1.0.1)

PoissonExpPower: Poisson Exponential Power Distribution

Description

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

Usage

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

Value

• dpois.exp.pow: numeric vector of (log-)densities

• ppois.exp.pow: numeric vector of probabilities

• qpois.exp.pow: numeric vector of quantiles

• rpois.exp.pow: numeric vector of random variates

• hpois.exp.pow: 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 Exponential Power distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Poisson Exponential Power distribution has CDF:

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

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

The following functions are included:

• dpois.exp.pow() — Density function

• ppois.exp.pow() — Distribution function

• qpois.exp.pow() — Quantile function

• rpois.exp.pow() — Random generation

• hpois.exp.pow() — Hazard function

References

Joshi, R. K., & Kumar, V. (2020). Poisson Exponential Power distribution: Properties and Application. International Journal of Mathematics & Computer Research, 8(11), 2152--2158. tools:::Rd_expr_doi("10.47191/ijmcr/v8i11.01")

Examples

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

# Data
x <- stress
# ML estimates
params = list(alpha=0.6976, beta=0.6395, lambda=7.8045)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = ppois.exp.pow, fit.line=TRUE)

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

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