BetaR {betareg}

Create a Beta Regression Distribution

Description

Class and methods for beta distributions in regression specification using the workflow from the distributions3 package.

Usage

BetaR(mu, phi)

Arguments

mu

numeric. The mean of the beta distribution.

phi

numeric. The precision parameter of the beta distribution.

Details

Alternative parameterization of the classic beta distribution in terms of its mean mu and precision parameter phi. Thus, the distribution provided by BetaR is equivalent to the Beta distribution with parameters alpha = mu * phi and beta = (1 - mu) * phi.

Value

A BetaR distribution object.

See Also

dbetar, Beta

Examples

## package and random seed
library("distributions3")
set.seed(6020)

## three beta distributions
X <- BetaR(
  mu  = c(0.25, 0.50, 0.75),
  phi = c(1, 1, 2)
)

X

## compute moments of the distribution
mean(X)
variance(X)
skewness(X)
kurtosis(X)

## support interval (minimum and maximum)
support(X)

## simulate random variables
random(X, 5)

## histograms of 1,000 simulated observations
x <- random(X, 1000)
hist(x[1, ])
hist(x[2, ])
hist(x[3, ])

## probability density function (PDF) and log-density (or log-likelihood)
x <- c(0.25, 0.5, 0.75)
pdf(X, x)
pdf(X, x, log = TRUE)
log_pdf(X, x)

## cumulative distribution function (CDF)
cdf(X, x)

## quantiles
quantile(X, 0.5)

## cdf() and quantile() are inverses (except at censoring points)
cdf(X, quantile(X, 0.5))
quantile(X, cdf(X, 1))

## all methods above can either be applied elementwise or for
## all combinations of X and x, if length(X) = length(x),
## also the result can be assured to be a matrix via drop = FALSE
p <- c(0.05, 0.5, 0.95)
quantile(X, p, elementwise = FALSE)
quantile(X, p, elementwise = TRUE)
quantile(X, p, elementwise = TRUE, drop = FALSE)

## compare theoretical and empirical mean from 1,000 simulated observations
cbind(
  "theoretical" = mean(X),
  "empirical" = rowMeans(random(X, 1000))
)