Beta prime distribution
Density, distribution function, quantile function and random generation for the beta prime distribution.
dbetapr(x, shape1, shape2, scale = 1, log = FALSE) pbetapr(q, shape1, shape2, scale = 1, lower.tail = TRUE, log.p = FALSE) qbetapr(p, shape1, shape2, scale = 1, lower.tail = TRUE, log.p = FALSE) rbetapr(n, shape1, shape2, scale = 1)
x, q |
vector of quantiles. |
shape1, shape2 |
non-negative parameters. |
scale |
positive valued scale parameter. |
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]. |
p |
vector of probabilities. |
n |
number of observations. If |
If X ~ Beta(α, β), then X/(1-X) ~ BetaPrime(α, β).
Probability density function
f(x) = ((x/σ)^(α-1) * (1 + x/σ)^(-α-β)) / (B(α,β) * σ)
Cumulative distribution function
F(x) = pbeta((x/σ)/(1+(x/σ)), α, β)
x <- rbetapr(1e5, 5, 3, 2) hist(x, 350, freq = FALSE, xlim = c(0, 100)) curve(dbetapr(x, 5, 3, 2), 0, 100, col = "red", add = TRUE, n = 500) hist(pbetapr(x, 5, 3, 2)) plot(ecdf(x), xlim = c(0, 100)) curve(pbetapr(x, 5, 3, 2), 0, 100, col = "red", add = TRUE, n = 500)
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