NeuDist (version 1.0.1)

PoissonInvSGZ: Poisson Inverse Shifted Gompertz (PISG) Distribution

Description

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

Usage

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

Value

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

• ppois.inv.sgz: numeric vector of probabilities

• qpois.inv.sgz: numeric vector of quantiles

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

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

The Poisson Inverse Shifted Gompertz distribution has CDF:

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

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

The following functions are included:

• dpois.inv.sgz() — Density function

• ppois.inv.sgz() — Distribution function

• qpois.inv.sgz() — Quantile function

• rpois.inv.sgz() — Random generation

• hpois.inv.sgz() — Hazard function

References

Sapkota, L. P., Kumar, V., Tekle, G., Alrweili, H., Mustafa, M. S., & Yusuf, M. (2025). Fitting Real Data Sets by a New Version of Gompertz Distribution. Modern Journal of Statistics, 1(1), 25--48. tools:::Rd_expr_doi("10.64389/mjs.2025.01109")

Examples

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

# Data
x <- fibers69  
# ML estimates
params = list(alpha=98.0893, beta=10.6326, lambda=2.1006)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = ppois.inv.sgz, fit.line=TRUE)

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

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