NeuDist (version 1.0.1)

PoissonInvNHE: Poisson Inverse NHE Distribution

Description

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

Usage

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

Value

• dpois.inv.NHE: numeric vector of (log-)densities

• ppois.inv.NHE: numeric vector of probabilities

• qpois.inv.NHE: numeric vector of quantiles

• rpois.inv.NHE: numeric vector of random variates

• hpois.inv.NHE: 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 Inverse NHE distribution is parameterized by the parameters \(\alpha > 0\), \(\beta > 0\), and \(\lambda > 0\).

The Poisson Inverse NHE distribution has CDF:

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

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

The following functions are included:

• dpois.inv.NHE() — Density function

• ppois.inv.NHE() — Distribution function

• qpois.inv.NHE() — Quantile function

• rpois.inv.NHE() — Random generation

• hpois.inv.NHE() — Hazard function

References

Chaudhary,A.K.& Kumar, V.(2020). Poisson Inverse NHE Distribution. International Journal of Science and Research(IJSR), 9(12), 1603--1610.

Examples

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

# Data
x <- fibers63
# ML estimates
params = list(alpha=1.0174, beta=5.1414, lambda=23.3476)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = ppois.inv.NHE, fit.line=TRUE)

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

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