Get functions from a distribution

[mbaudin47]

What happened?

In #2759, we implement Distribution.getPDF() and Distribution.getCDF() which return the ot.Function corresponding to the PDF or CDF. This feature is interesting for various cases, e.g. compute or draw the likelihood of a sample with respect to the parameters of a distribution. This principle also applies to other objects from a distribution :

• logPDF
• quantile
• survival
• covariance
• shiftedMoment
• conditionalPDF
• conditionalCDF
• entropyKernel
• PDFSquared

In this list, not all functions are required in practice.

• In order to evaluate or draw the likelihood of a sample, the logPDF() function is interesting. Notice that this use-case could be implemented as a new method of the MaximumLikelihoodFactory.getLikelihood(). If we have the logPDF, then we can use a custom optimizer algorithm. Notice that this can be done based on a user-defined PythonFunction.

import openturns as ot
distribution = ot.Normal()
sample = distribution.getSample(10)
logpdf = distribution.getLogPDF()
ylog = logpdf(sample)  # Use case 1
logpdf.draw(xMin, xMax)  # Use case 2

• We could easily draw the quantile function:

import openturns as ot
distribution = ot.Normal()
sample = distribution.getSample(10)
quantilefunction= distribution.getQuantile()
quantilefunction.draw(xMin, xMax)  # Use case 3

Version

1.23

Operating System

unknown

Installation media

unknown

Additional Context

No response