ggstacy: The Generalized Gamma Distribution (Stacy's original...

In survstan: Fitting Survival Regression Models via 'Stan'

The Generalized Gamma Distribution (Stacy's original parametrization)

Description

Probability function, distribution function, quantile function and random generation for the distribution with parameters alpha, gamma and kappa.

Usage

dggstacy(x, alpha, gamma, kappa, log = FALSE)

pggstacy(q, alpha, gamma, kappa, log.p = FALSE, lower.tail = TRUE)

qggstacy(
  p,
  alpha = 1,
  gamma = 1,
  kappa = 1,
  log.p = FALSE,
  lower.tail = TRUE,
  ...
)

rggstacy(n, alpha = 1, gamma = 1, kappa = 1, ...)

Arguments

x	vector of (non-negative integer) quantiles.
alpha	shape parameter of the distribution (alpha > 0).
gamma	scale parameter of the distribution (gamma > 0).
kappa	shape parameter of the distribution (kappa > 0).
log, log.p	logical; if TRUE, probabilities p are given as log(p).
q	vector of quantiles.
lower.tail	logical; if TRUE (default), probabilities are P[X \le x]; otherwise, P[X > x].
p	vector of probabilities.
...	further arguments passed to other methods.
n	number of random values to return.

Details

Probability density function:

f(x|\alpha, \gamma, \kappa) = \frac{\kappa}{\gamma^{\alpha}\Gamma(\alpha/\kappa)}x^{\alpha-1}\exp\left\{-\left(\frac{x}{\gamma}\right)^{\kappa}\right\}I_{[0, \infty)}(x),

for \alpha>0, \gamma>0 and \kappa>0.

Distribution function:

F(t|\alpha, \gamma, \kappa) = F_{G}(x|\nu, 1),

where x = \displaystyle\left(\frac{t}{\gamma}\right)^\kappa, and F_{G}(\cdot|\nu, 1) corresponds to the distribution function of a gamma distribution with shape parameter \nu = \alpha/\gamma and scale parameter equals to 1.

Value

dggstacy gives the (log) probability function, pggstacy gives the (log) distribution function, qggstacy gives the quantile function, and rggstacy generates random deviates.

survstan documentation built on May 29, 2024, 8:41 a.m.