Density, distribution function, quantile function and random
generation for the GB1 distribution with parameters shape0,
shape1 and shape2.
dgbeta(x, shape0, shape1, shape2, log = FALSE)
pgbeta(q, shape0, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
qgbeta(p, shape0, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
rgbeta(n, shape0, shape1, shape2)
ecgbeta(x, shape0, shape1, shape2)
mgbeta(order, shape0, shape1, shape2)dgbeta gives the density, pgbeta the distribution
function, qgbeta the quantile function, and rgbeta
generates random deviates.
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length
is taken to be the number required.
positive parameters of the GB1 distribution.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).
order of the raw moment.
The GB1 distribution with parameters shape0 \(= g\),
shape1 \(= a\) and shape2 \(= b\) has density
$$f(x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}{x}^{a/g-1} {(1-x^{1/g})}^{b-1}/g%
$$
for \(a,b,g > 0\) and \(0 \le x \le 1\)
where the boundary values at \(x=0\) or \(x=1\) are defined as
by continuity (as limits).
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language, Wadsworth & Brooks/Cole, tools:::Rd_expr_doi("10.1201/9781351074988").
Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions. New York: Dover. Chapter 6: Gamma and Related Functions.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, Volume 2, especially Chapter 25. Wiley, New York, tools:::Rd_expr_doi("10.1080/00224065.1996.11979675").
Distributions for other standard distributions.
#density
curve(dgbeta(x, 3, 2, 3))
#cdf
curve(pgbeta(x, 3, 2, 3))
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