BAMLSS {bamlss}  R Documentation 
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, ...)
Arguments
family 
object. BAMLSS family specifications recognized by

... 
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.
Value
A BAMLSS
distribution object.
See Also
Examples
## 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 logdensity (or loglikelihood)
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))
## )