ggstacy | R Documentation |
Probability function, distribution function, quantile function and random generation for the distribution with parameters alpha, gamma and kappa.
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, ...)
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 |
vector of probabilities. |
... |
further arguments passed to other methods. |
n |
number of random values to return. |
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.
dggstacy gives the (log) probability function, pggstacy gives the (log) distribution function, qggstacy gives the quantile function, and rggstacy generates random deviates.
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