I have a data, which looks like mixture of $\gamma$ and Gausian distributions: enter image description here

Could you help me to find parameters of these distributions?


1 Answer 1


The answer depends on what software is used for fitting and what error measure is minimized when fitting the distributions.

As an example, STAN reference (v2.14.0) provides details on fitting finite mixtures in chapter 12.

Here is a simple code draft adapted for fitting a mixture of Gaussian and Gamma distribution.

data {
    int<lower=1> N;  // number of data points
    real y[N]; // observations
parameters {
    simplex[2] theta;// mixing proportions
    real phi[4]; // distribution parameters
model {
    real ps[2]; // temp for log component densities
    for (n in 1:N) {
        ps[1] = log(theta[1])+ normal_lpdf(y[n] | phi[1], phi[2]);
        ps[2] = log(theta[2])+ gamma_lpdf(y[n] | phi[3], phi[4]);
        target += log_sum_exp(ps);

The code computes

$p(y|\phi,\theta_1)= \sum_{i=1}^N\log(\theta_1) \mathrm{PDF}_\mathrm{Normal}(y_i|\phi_1,\phi_2) +\log(1-\theta_1) \mathrm{PDF}_\mathrm{Gamma}(y_i|\phi_3,\phi_4) $

and adds it to the log density of the MCMC sampling algorithm.


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