NeuDist (version 1.0.1)

InvGenGPZ: Inverse Generalized Gompertz Distribution

Description

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

Usage

dinv.gen.gpz(x, alpha, lambda, theta, log = FALSE)
pinv.gen.gpz(q, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
qinv.gen.gpz(p, alpha, lambda, theta, lower.tail = TRUE, log.p = FALSE)
rinv.gen.gpz(n, alpha, lambda, theta)
hinv.gen.gpz(x, alpha, lambda, theta)

Value

• dinv.gen.gpz: numeric vector of (log-)densities

• pinv.gen.gpz: numeric vector of probabilities

• qinv.gen.gpz: numeric vector of quantiles

• rinv.gen.gpz: numeric vector of random variates

• hinv.gen.gpz: 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 Inverse Generalized Gompertz distribution is parameterized by the parameters \(\alpha > 0\), \(\lambda > 0\), and \(\theta > 0\).

The Inverse Generalized Gompertz distribution has CDF:

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

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

The implementation includes the following functions:

• dinv.gen.gpz() — Density function

• pinv.gen.gpz() — Distribution function

• qinv.gen.gpz() — Quantile function

• rinv.gen.gpz() — Random generation

• hinv.gen.gpz() — Hazard function

References

Chaudhary, A.K., & Kumar, V. (2017). Inverse Generalized Gompertz Distribution with Properties and Applications. Journal of National Academy of Mathematics, 31, 1--15.

Examples

x <- seq(2, 5, 0.25)
dinv.gen.gpz(x, 1.5, 2.5, 5.0)
pinv.gen.gpz(x, 1.5, 2.5, 5.0)
qinv.gen.gpz(0.5, 1.5, 2.5, 5.0)
rinv.gen.gpz(10, 1.5, 2.5, 5.0)
hinv.gen.gpz(x, 1.5, 2.5, 5.0)

# Data
x <- fibers63
# ML estimates
params = list(alpha=3.4106, lambda=5.4685, theta=20.9199)
#P–P (probability–probability) plot
pp.plot(x, params = params, pfun = pinv.gen.gpz, fit.line=TRUE)

#Q-Q (quantile–quantile) plot 
qq.plot(x, params = params, qfun = qinv.gen.gpz, fit.line=TRUE)

# Goodness-of-Fit(GoF) and Model Diagnostics 
out <- gofic(x, params = params,
             dfun = dinv.gen.gpz, pfun=pinv.gen.gpz, plot=TRUE)
print.gofic(out)