What is the relationship between real Gaussian Mixture Density function and gmdistribution?

the Gaussian Mixture Density function is defined as a sum of weighted normal density functions for each component. Using gmdistribution.fit, we can obtain all the parameters like Sigma, Weights and mean for each component. Problem is, constructing the Gaussian Mixture Density function using those parameters is not as the same as the result calculated by the build-in Probability density function for Gaussian mixture distribution in Matlab. Why is this the case? What is the relationship between the properties calculated by gmdistribution.fit and the parameters in a real Gaussian Mixture Probability Density function?

By the way, what I want is to find the formula of Gaussian Mixture Probability Density function by fitting the corresponding dataset.

Answer 1

[Jang Bahadur Singh]

use: pdf help from File Exchange: gmm_fit.m