ReferenceMeasureTransformed: A general continuous reference measure on the real line

In DistributionalDDA: Distributional Data Analysis in Bayes Spaces

A general continuous reference measure on the real line

Description

The reference measure is created by transforming a ReferenceMeasure Uniform to a given distributions based using a distribution function and a quantile function.

Usage

ReferenceMeasureTransformed(
  cdf = c("pnorm", "pbeta", "pcauchy", "pchisq", "pexp", "pf", "pgamma", "plnorm",
    "plogis", "pt", "punif", "pweibull", "pwilcox"),
  qf = cdf2qf(cdf, ...),
  ...,
  pdf = cdf2density(cdf, ...),
  reference = StdReferenceMeasureUnif01,
  .args = list(...),
  .eps = 1e-07
)

## S3 method for class 'ReferenceMeasureTransformed'
getSample(x, ...)

Arguments

cdf	the cumulative distribution function of the reference measure. For the standard distributions listed as default argument, it can be provided as a string. In this case the corresponding quantile and density functions are selected automatically. The distribution parameters should be provided in ...
qf	the corresponding quantile function, mapping a value of the reference measure to its quantiles.
...	further arguments for cdf, qf, and lebesgue_density
pdf	a function representing the Lebesgue Density (aka as probability density function) of the measure, for conversion to and from pdfs.
reference	the underlying untransformed reference measure to be used
.args	the list of further arguments to cdf and qf
.eps	the precision to check the roundtrip between
x	a ReferenceMeasureTransformed object

Value

a reference measure with representing the reference measure described by the distribution and quantile function.

Methods (by generic)

• getSample(ReferenceMeasureTransformed): returns transformed sample from the underlying reference

See Also

Other ReferenceMeasures: B2N01, ReferenceMeasureDiscrete(), ReferenceMeasureUniform(), StdReferenceMeasureUnif01, expectation(), getSample(), isInDomain()

Examples

rmt = ReferenceMeasureTransformed(pnorm,qnorm,mean=2,sd=2)
isInDomain(0:17,rmt)
expectation(rmt,\(x) x^2)
hist(getSample(rmt))

DistributionalDDA documentation built on Oct. 20, 2026, 5:06 p.m.