cdf

Cumulative distribution function for Gaussian mixture distribution

Syntax

y = cdf(gm,X)

Description

y = cdf(gm,X) returns the cumulative distribution function (cdf) of the Gaussian mixture distribution gm, evaluated at the values in X.

Examples

Compute cdf Values

Create a gmdistribution object and compute its cdf values.

Define the distribution parameters (means and covariances) of a two-component bivariate Gaussian mixture distribution.

mu = [1 2;-3 -5];
sigma = [1 1]; % shared diagonal covariance matrix

Create a gmdistribution object by using the gmdistribution function. By default, the function creates an equal proportion mixture.

gm = gmdistribution(mu,sigma)

gm = 

Gaussian mixture distribution with 2 components in 2 dimensions
Component 1:
Mixing proportion: 0.500000
Mean:     1     2

Component 2:
Mixing proportion: 0.500000
Mean:    -3    -5

Compute the cdf values of gm.

X = [0 0;1 2;3 3;5 3];
cdf(gm,X)

ans = 4×1

    0.5011
    0.6250
    0.9111
    0.9207

Plot cdf

Create a gmdistribution object and plot its cdf.

Define the distribution parameters (means, covariances, and mixing proportions) of two bivariate Gaussian mixture components.

p = [0.4 0.6];               % Mixing proportions     
mu = [1 2;-3 -5];            % Means
sigma = cat(3,[2 .5],[1 1])  % Covariances 1-by-2-by-2 array

sigma = 
sigma(:,:,1) =

    2.0000    0.5000


sigma(:,:,2) =

     1     1

The cat function concatenates the covariances along the third array dimension. The defined covariance matrices are diagonal matrices. sigma(1,:,i) contains the diagonal elements of the covariance matrix of component i.

Create a gmdistribution object by using the gmdistribution function.

gm = gmdistribution(mu,sigma,p)

gm = 

Gaussian mixture distribution with 2 components in 2 dimensions
Component 1:
Mixing proportion: 0.400000
Mean:     1     2

Component 2:
Mixing proportion: 0.600000
Mean:    -3    -5

Plot the cdf of the Gaussian mixture distribution by using fsurf.

gmCDF = @(x,y) arrayfun(@(x0,y0) cdf(gm,[x0 y0]),x,y);
fsurf(gmCDF,[-10 10])

Input Arguments

gm — Gaussian mixture distribution

gmdistribution object

Gaussian mixture distribution, also called Gaussian mixture model (GMM), specified as a gmdistribution object.

You can create a gmdistribution object using gmdistribution or fitgmdist. Use the gmdistribution function to create a gmdistribution object by specifying the distribution parameters. Use the fitgmdist function to fit a gmdistribution model to data given a fixed number of components.

X — Values at which to evaluate cdf

n-by-m numeric matrix

Values at which to evaluate the cdf, specified as an n-by-m numeric matrix, where n is the number of observations and m is the number of variables in each observation.

Data Types: single | double

Output Arguments

y — cdf values

n-by-1 numeric vector

cdf values of the Gaussian mixture distribution gm, evaluated at X, returned as an n-by-1 numeric vector, where n is the number of observations in X.