Nonparametric Statistical Distributions

When building an initial statistical model, you may not have a good idea of what parametric distribution family it should come from. Nonparametric distributions make very few assumptions about the underlying model so can be used for a wide variety of situations. Nonparametric distributions are based on familiar methods such as histograms and kernel density estimators. The resulting distributions work just like any other distribution in that you can generate random variates, compute moments and quantiles, or compute full distribution functions. Different nonparametric distributions essentially provide different levels and methods of smoothing.

Empirical Distribution

EmpiricalDistribution distribution constructed from all data

DiscretePlot  ▪  Tally

Histogram Distribution

HistogramDistribution distribution constructed from binning of data

Histogram  ▪  HistogramList

Smooth Kernel Distributions

SmoothKernelDistribution distribution with interpolated distribution functions

KernelMixtureDistribution distribution with mixture distribution functions

SmoothHistogram  ▪  MixtureDistribution

Distributions from Censored Data

SurvivalDistribution empirical distribution from censored data

SurvivalModelFit survival distribution with confidence intervals

CoxModelFit survival distribution with independent variables

Nonparametric Distribution Object

DataDistribution distribution object generated by nonparametric distributions

InterpolationPoints  ▪  MaxMixtureKernels  ▪  MaxExtraBandwidths

Machine-Learning Distributions

LearnedDistribution distribution for any kind of data (numerical, images, ...)

LearnDistribution  ▪  PredictorFunction  ▪  ClassifierFunction  ▪  ...