PiecewiseLinearDistribution

Piecewise linear probability distribution object

Description

A PiecewiseLinearDistribution object consists of a model description for a piecewise linear probability distribution.

The piecewise linear distribution is a nonparametric probability distribution created using a piecewise linear representation of the cumulative distribution function (cdf). The options specified for the piecewise linear distribution specify the form of the cdf. The probability density function (pdf) is a step function.

The piecewise linear distribution uses the following parameters.

Parameter	Description
x	Vector of x values at which the cdf changes slope
Fx	Vector of cdf values that correspond to each value in x

Creation

Create a PiecewiseLinearDistribution probability distribution with specified parameter values object using makedist.

Properties

Distribution Parameters

x — Data values

vector of scalar values

Data values at which the cumulative distribution function (cdf) changes slope, specified as a vector of scalar values.

Data Types: single | double

Fx — cdf values

vector of scalar values

cdf value at each value in x, specified as a vector of scalar values.

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

NumParameters — Number of parameters

positive integer value

This property is read-only.

Number of parameters for the probability distribution, specified as a positive integer value.

Data Types: double

ParameterValues — Distribution parameter values

vector of scalar values

This property is read-only.

Distribution parameter values, specified as a vector of scalar values.

Data Types: single | double

Truncation — Truncation interval

vector of scalar values

This property is read-only.

Truncation interval for the probability distribution, specified as a vector of scalar values 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

ParameterDescription — Distribution parameter descriptions

cell array of character vectors

This property is read-only.

Distribution parameter descriptions, specified as a cell array of character vectors. Each cell contains a short description of one distribution parameter.

Data Types: char

ParameterNames — Distribution parameter names

cell array of character vectors

This property is read-only.

Distribution parameter names, specified as a cell array of character vectors.

Data Types: char

Object Functions

cdf	Cumulative distribution function
icdf	Inverse cumulative distribution function
iqr	Interquartile range of probability distribution
mean	Mean of probability distribution
median	Median 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

Create a Piecewise Linear Distribution Object Using Default Parameters

Create a piecewise linear distribution object using the default parameter values.

pd = makedist('PiecewiseLinear')

pd = 
  PiecewiseLinearDistribution

F(0) = 0
F(1) = 1

Create Piecewise Linear Distribution Object from Empirical cdf

Compute the empirical cumulative distribution function (cdf) for data, and create a piecewise linear distribution object using an approximation to the empirical cdf.

Load the sample data. Visualize the patient weight data using a histogram.

load patients
histogram(Weight(strcmp(Gender,'Female')))
hold on
histogram(Weight(strcmp(Gender,'Male')))
legend('Female','Male')

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

Compute the empirical cdf for the data.

[f,x] = ecdf(Weight);

Construct a piecewise linear approximation to the empirical cdf by taking a value every five points.

f = f(1:5:end);
x = x(1:5:end);

Plot the empirical cdf and the approximation.

figure
ecdf(Weight)
hold on
plot(x,f,'ko-','MarkerFace','r') 
legend('Empirical cdf','Piecewise linear approximation', ...
    'Location','best')

Create a piecewise linear probability distribution object using the piecewise approximation of the empirical cdf.

pd = makedist('PiecewiseLinear','x',x,'Fx',f)

pd = 
  PiecewiseLinearDistribution

F(111) = 0
F(118) = 0.05
F(124) = 0.13
F(130) = 0.25
F(135) = 0.37
F(142) = 0.5
F(163) = 0.55
F(171) = 0.61
F(178) = 0.7
F(183) = 0.82
F(189) = 0.94
F(202) = 1

Generate 100 random numbers from the distribution.

rng('default') % For reproducibility
rw = random(pd,[100,1]);

Plot the random numbers to visually compare their distribution to the original data.

figure
histogram(Weight)
hold on
histogram(rw)
legend('Original data','Generated data')

The random numbers generated from the piecewise linear distribution have the same bimodal distribution as the original data.

Version History

Introduced in R2013a