pdf1d : Univariate Probability Density Function Library

Introduction

Provides several classes for representing and using univariate probability density functions (PDFs).

Each PDF comes as a builder-model-sampler triplet of objects.

e.g. The abstract PDF base classes

• pdf1d_pdf (Represents a PDF)
• pdf1d_sampler (Generate random samples from a pdf)
• pdf1d_builder (Build a pdf from some data)

For instance, the univariate Gaussian PDF classes

• pdf1d_gaussian
• pdf1d_gaussian_sampler
• pdf1d_gaussian_builder

A variety of types of simple PDF are implemented:

• pdf1d_flat (Flat distribution over a range)
• pdf1d_gaussian
• pdf1d_exponential (Exponential distribution $p(x)= exp(- x)$)

The models are used to calculate densities, cumulative probabilities, gradients, etc.

Kernel Estimates

The classes

• pdf1d_kernel_pdf
• pdf1d_kernel_pdf_builder

Are kernel PDFs, ie representing a PDF by placing a kernel at every point in a sample. The builder includes a variety of algorithms taken from "Density Estimation" by B.W.Silverman (Pub. Chapman and Hall, 1986), including a recommended choice of kernel width and an implementation of the adaptive kernel estimate.

Examples of kernels available include

• pdf1d_gaussian_kernel_pdf
• pdf1d_epanech_kernel_pdf (Epanechnikov kernel - quadratic)

Mixture Models

Mixture models are represented using the pdf1d_mixture class. The pdf1d_mixture_builder uses the EM algorithm to estimate the parameters of the mixtures.