| Title: | Generalized Beta and Beta Prime Distributions |
|---|---|
| Description: | Density, distribution function, quantile function, and random generation for the generalized Beta and Beta prime distributions. The family of generalized Beta distributions is conjugate for the Bayesian binomial model, and the generalized Beta prime distribution is the posterior distribution of the relative risk in the Bayesian 'two Poisson samples' model when a Gamma prior is assigned to the Poisson rate of the reference group and a Beta prime prior is assigned to the relative risk. References: Laurent (2012) <doi:10.1214/11-BJPS139>, Hamza & Vallois (2016) <doi:10.1016/j.spl.2016.03.014>, Chen & Novick (1984) <doi:10.3102/10769986009002163>. |
| Authors: | Stéphane Laurent |
| Maintainer: | Stéphane Laurent <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1.0 |
| Built: | 2024-11-15 04:51:54 UTC |
| Source: | https://github.com/stla/gbeta |
Density, distribution function, quantile function, and random generation for the generalized Beta distribution.
dgbeta(u, c, d, kappa, tau, log = FALSE) pgbeta(q, c, d, kappa, tau) rgbeta(n, c, d, kappa, tau, method = "mixture") qgbeta(p, c, d, kappa, tau)dgbeta(u, c, d, kappa, tau, log = FALSE) pgbeta(q, c, d, kappa, tau) rgbeta(n, c, d, kappa, tau, method = "mixture") qgbeta(p, c, d, kappa, tau)
u |
numeric vector |
c, d, kappa, tau
|
parameters; they must be strictly positive numbers,
except |
log |
logical, whether to return the log-density |
q |
numeric vector of quantiles |
n |
positive integer, the desired number of simulations |
method |
the method of random generation, |
p |
numeric vector of probabilities |
Marwa Hamza & Pierre Vallois. On Kummer’s distributions of type two and generalized Beta distributions. Statistics & Probability Letters 118 (2016), pp. 60-69. <doi:10.1016/j.spl.2016.03.014>
James J. Chen & Melvin R. Novick. Bayesian Analysis for Binomial Models with Generalized Beta Prior Distributions. Journal of Educational Statistics 9, No. 2 (1984), pp. 163-175. <doi:10.3102/10769986009002163>
library(gbeta) curve(dgbeta(x, 4, 12, 10, 0.01), axes = FALSE, lwd = 2) axis(1)library(gbeta) curve(dgbeta(x, 4, 12, 10, 0.01), axes = FALSE, lwd = 2) axis(1)
Density, distribution function, quantile function, and random generation for the generalized Beta prime distribution.
dgbetap(x, c, d, kappa, tau, scale = 1, log = FALSE) pgbetap(q, c, d, kappa, tau, scale = 1) rgbetap(n, c, d, kappa, tau, scale = 1, method = "mixture") qgbetap(p, c, d, kappa, tau, scale = 1)dgbetap(x, c, d, kappa, tau, scale = 1, log = FALSE) pgbetap(q, c, d, kappa, tau, scale = 1) rgbetap(n, c, d, kappa, tau, scale = 1, method = "mixture") qgbetap(p, c, d, kappa, tau, scale = 1)
x |
numeric vector |
c, d, kappa, tau
|
parameters; they must be strictly positive numbers,
except |
scale |
scale parameter, a strictly positive number |
log |
logical, whether to return the log-density |
q |
numeric vector of quantiles |
n |
positive integer, the desired number of simulations |
method |
the method of random generation, |
p |
numeric vector of probabilities |
Stéphane Laurent. Some Poisson mixtures distributions with a hyperscale parameter. Brazilian Journal of Probability and Statistics 26, No. 3 (2012), pp. 265-278. <doi:10.1214/11-BJPS139>
Myriam Chabot. Sur l’estimation du rapport de deux paramètres d’intensité poissonniens et l’estimation par fonctions de masse prédictives. Master thesis. Université de Scherbrooke, 2016.
library(gbeta) curve(dgbetap(x, 4, 12, 10, 0.01), to = 10, axes = FALSE, lwd = 2) axis(1)library(gbeta) curve(dgbetap(x, 4, 12, 10, 0.01), to = 10, axes = FALSE, lwd = 2) axis(1)