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

0 | 1

This property is read-only.

Logical flag for truncated distribution, specified as a logical value. If IsTruncated equals 0, the distribution is not truncated. If IsTruncated equals 1, the distribution is truncated.

Data Types: logical

Truncation — Truncation interval

vector of scalar values

This property is read-only.

Truncation interval for the probability distribution, specified as a vector containing the lower and upper truncation boundaries.

Data Types: single | double

Other Object Properties

DistributionName — Probability distribution name

character vector

This property is read-only.

Probability distribution name, specified as a character vector.

Data Types: char

InputData — Data used for distribution fitting

structure

This property is read-only.

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

• data: Data vector used for distribution fitting.

• cens: Censoring vector, or empty if none.

• freq: Frequency vector, or empty if none.

Data Types: struct

Object Functions

cdf	Cumulative distribution function
icdf	Inverse cumulative distribution function
iqr	Interquartile range
mean	Mean of probability distribution
median	Median of probability distribution
negloglik	Negative loglikelihood of probability distribution
pdf	Probability density function
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. Visualize the patient weight data using a histogram.

load hospital
histogram(hospital.Weight)

The histogram shows that the data has two modes, one for female patients and one for male patients.

Create a probability distribution object by fitting a kernel distribution to the patient weight data.

pd_kernel = fitdist(hospital.Weight,'Kernel')

pd_kernel = 
  KernelDistribution

    Kernel = normal
    Bandwidth = 14.3792
    Support = unbounded

For comparison, create another probability distribution object by fitting a normal distribution to the patient weight data.

pd_normal = fitdist(hospital.Weight,'Normal')

pd_normal = 
  NormalDistribution

  Normal distribution
       mu =     154   [148.728, 159.272]
    sigma = 26.5714   [23.3299, 30.8674]

Define the x values and compute the pdf of each distribution.

x = 50:1:250;
pdf_kernel = pdf(pd_kernel,x);
pdf_normal = pdf(pd_normal,x);

Plot the pdf of each distribution.

plot(x,pdf_kernel,'Color','b','LineWidth',2);
hold on;
plot(x,pdf_normal,'Color','r','LineStyle',':','LineWidth',2);
legend('Kernel Distribution','Normal Distribution','Location','SouthEast');
hold off;

Fitting a kernel distribution instead of a unimodal distribution such as the normal reveals the separate modes for the female and male patients.