Density, distribution function, quantile function and random
generation for the GB1 distribution with parameters shape0
,
shape1
and shape2
.
1 2 3 4 5 6 
x, q 
vector of quantiles. 
p 
vector of probabilities. 
n 
number of observations. If 
shape0, shape1, shape2 
positive parameters of the GB1 distribution. 
log, log.p 
logical; if TRUE, probabilities p are given as log(p). 
lower.tail 
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. 
order 
order of the raw moment. 
The GB1 distribution with parameters shape0
= g,
shape1
= a and shape2
= b has density
Γ(a+b)/(Γ(a)Γ(b))x^(a/g1)(1x^{1/g})^(b1)/g
for a,b,g > 0 and 0 ≤ x ≤ 1 where the boundary values at x=0 or x=1 are defined as by continuity (as limits).
dgbeta
gives the density, pgbeta
the distribution
function, qgbeta
the quantile function, and rgbeta
generates random deviates.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
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.
Distributions for other standard distributions.
1  #TODO

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