BAMLSS: Create distributions3 Object

Description

A single class and corresponding methods encompassing all bamlss.family distributions (from the bamlss package) using the workflow from the distributions3 package.

Usage

BAMLSS(family, ...)

Value

A BAMLSS distribution object.

Arguments

family: object. BAMLSS family specifications recognized by bamlss.family, including family.bamlss objects, family-generating functions (e.g., gaussian_bamlss), or characters with family names (e.g., "gaussian" or "binomial").
...: further arguments passed as parameters to the BAMLSS family. Can be scalars or vectors.

Details

The constructor function BAMLSS sets up a distribution object, representing a distribution from the BAMLSS (Bayesian additive model of location, scale, and shape) framework by the corresponding parameters plus a family attribute, e.g., gaussian_bamlss for the normal distribution or binomial_bamlss for the binomial distribution. The parameters employed by the family vary across the families but typically capture different distributional properties (like location, scale, shape, etc.).

All parameters can also be vectors, so that it is possible to define a vector of BAMLSS distributions from the same family with potentially different parameters. All parameters need to have the same length or must be scalars (i.e., of length 1) which are then recycled to the length of the other parameters.

For the BAMLSS distribution objects there is a wide range of standard methods available to the generics provided in the distributions3 package: pdf and log_pdf for the (log-)density (PDF), cdf for the probability from the cumulative distribution function (CDF), quantile for quantiles, random for simulating random variables, and support for the support interval (minimum and maximum). Internally, these methods rely on the usual d/p/q/r functions provided in bamlss, see the manual pages of the individual families. The methods is_discrete and is_continuous can be used to query whether the distributions are discrete on the entire support or continuous on the entire support, respectively.

See the examples below for an illustration of the workflow for the class and methods.

Examples

Run this code

 if(!requireNamespace("bamlss")) {
  if(interactive() || is.na(Sys.getenv("_R_CHECK_PACKAGE_NAME_", NA))) {
    stop("not all packages required for the example are installed")
  } else q() }

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

## three Weibull distributions
X <- BAMLSS("weibull", lambda = c(1, 1, 2), alpha = c(1, 2, 2))
X

## moments (FIXME: mean and variance not provided by weibull_bamlss)
## mean(X)
## variance(X)

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

## simulate random variables
random(X, 5)

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

## probability density function (PDF) and log-density (or log-likelihood)
x <- c(2, 2, 1)
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
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
## (FIXME: mean not provided by weibull_bamlss)
## cbind(
##   "theoretical" = mean(X),
##   "empirical" = rowMeans(random(X, 1000))
## )