gamlss2

Create a GDF Distribution

Description

The GDF (gamlss2 Distribution Family) is a unified class with corresponding methods that represent all distributional families supported by the gamlss2 package. It enables seamless integration with the distributions3 workflow and provides a consistent interface for model fitting and distributional computations.

Usage

GDF(family, parameters)

Arguments

family character. Name of a gamlss2.family or a family provided by the gamlss.dist package, e.g, NO or BI for the normal or binomial distribution, respectively.

parameters numeric, matrix, list or data frame, see the examples.

Details

The S3 class GDF is a slightly more general implementation of the S3 class GAMLSS tailored for gamlss2. For details please see the documentation of GAMLSS

Value

A GDF object, inheriting from distribution.

References

Zeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.

Examples

library("gamlss2")


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

## one normal distribution
X <- GDF("NO", c(mu = 1, sigma = 2))
X

[1] "GDF NO(mu = 1, sigma = 2)"

## two normal distributions
X <- GDF("NO", cbind(c(1, 1.5), c(0.6, 1.2)))
X

[1] "GDF NO(mu = 1.0, sigma = 0.6)" "GDF NO(mu = 1.5, sigma = 1.2)"

## three Weibull distributions
X <- GDF("WEI", list(mu = c(1, 1, 2), sigma = c(1, 2, 2)))
X

[1] "GDF WEI(mu = 1, sigma = 1)" "GDF WEI(mu = 1, sigma = 2)"
[3] "GDF WEI(mu = 2, sigma = 2)"

## see ?gamlss.dist::GAMLSS for the remainder of this example

## example using gamlss2
data("abdom", package = "gamlss.data")

## estimate model
b <- gamlss2(y ~ s(x) | . | . | ., data = abdom, family = GA)

GAMLSS-RS iteration  1: Global Deviance = 4937.7817 eps = 0.369951     
GAMLSS-RS iteration  2: Global Deviance = 4789.2637 eps = 0.030077     
GAMLSS-RS iteration  3: Global Deviance = 4781.6786 eps = 0.001583     
GAMLSS-RS iteration  4: Global Deviance = 4781.3298 eps = 0.000072     
GAMLSS-RS iteration  5: Global Deviance = 4781.3279 eps = 0.000000

## extract, also works with newdata
d <- data.frame(
  "mean" = mean(b),
  "median" = median(b),
  "q95" = quantile(b, probs = 0.95),
  "variance" = variance(b),
  "pdf" = pdf(b),
  "cdf" = cdf(b)
)
print(head(d))

      mean   median      q95 variance        pdf        cdf
1 63.88365 63.68775 74.28810 37.56522 0.05039650 0.21597227
2 63.88365 63.68775 74.28810 37.56522 0.06491059 0.52031921
3 63.88365 63.68775 74.28810 37.56522 0.03009676 0.09492411
4 65.19952 65.00336 75.71423 38.38753 0.05409279 0.25428282
5 67.91225 67.71560 78.65099 40.08579 0.03735092 0.83274464
6 67.91225 67.71560 78.65099 40.08579 0.03054142 0.10196647