KernelDistribution

Kernel probability distribution object

Description

A KernelDistribution object consists of parameters, a model description, and sample data for a nonparametric kernel-smoothing distribution.

The kernel distribution is a nonparametric estimation of the probability density function (pdf) of a random variable.

The kernel distribution uses the following options.

Option	Description	Possible Values
Kernel	Kernel function type	normal, box, triangle, epanechnikov
Bandwidth	Kernel smoothing parameter	Bandwidth > 0

Creation

There are several ways to create a KernelDistribution probability distribution object.

• Fit a distribution to data using fitdist.

• Interactively fit a distribution to data using the Distribution Fitter app.

Properties

Distribution Parameters

Kernel — Kernel smoother type

'normal' | 'box' | 'triangle' | 'epanechnikov'

Kernel function type, specified as a valid kernel function type name.

Bandwidth — Bandwidth of kernel smoothing window

positive scalar value

Bandwidth of the kernel smoothing window, specified as a positive scalar value.

Data Types: single | double

Distribution Characteristics

IsTruncated — Logical flag for truncated distribution

Read-only: 0 (default) | 1

This property is read-only.

Logical flag for a truncated distribution, represented as 0 or 1. If IsTruncated is 0, the distribution is not truncated. If IsTruncated is 1, the distribution is truncated.

Data Types: logical

Truncation — Truncation interval

Read-only: vector of numeric scalars

This property is read-only.

Truncation interval for the probability distribution, represented as a vector of numeric scalars containing the lower and upper truncation boundaries.

Data Types: single | double

Other Object Properties

DistributionName — Probability distribution name

Read-only: character vector

This property is read-only.

Probability distribution name, represented as a character vector.

Data Types: char

InputData — Data used for distribution fitting

Read-only: structure

This property is read-only.

Data used for distribution fitting, represented as a structure containing the following:

• data – Data vector used for distribution fitting

• cens – Censoring vector (empty if none)

• freq – Frequency vector (empty if none)

Data Types: struct

Object Functions

cdf	Cumulative distribution function
gather	Gather properties of Statistics and Machine Learning Toolbox object from GPU
icdf	Inverse cumulative distribution function
iqr	Interquartile range of probability distribution
mean	Mean of probability distribution
median	Median of probability distribution
negloglik	Negative loglikelihood of probability distribution
pdf	Probability density function
plot	Plot probability distribution object
random	Random numbers
std	Standard deviation of probability distribution
truncate	Truncate probability distribution object
var	Variance of probability distribution

Examples

Fit a Kernel Distribution Object to Data

Load the sample data.

load carsmall

The variable MPG contains data for car gas mileage.

Create a probability distribution object by fitting a kernel distribution to MPG.

pd = fitdist(MPG,"Kernel")

pd = 
  KernelDistribution

    Kernel = normal
    Bandwidth = 4.11428
    Support = unbounded

pd is a probability distribution object with properties that include specifications for the kernel smoother type, bandwidth of the kernel smoothing window, and input data.

Plot the kernel pdf with a histogram of the input data.

plot(pd)

The plot shows the pdf of the kernel distribution fit to the MPG data. The distribution is smooth and slightly skewed with a heavier right tail.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• KernelDistribution can be a probability distribution object fitted by using fitdist with GPU array input arguments.

• The object functions of KernelDistribution fully support GPU arrays.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2013a