MATLAB: Random numbers from custom mixture distribution

gammalognormalmixurerandom

I would like to generate random numbers from a mixture distribution defined as,

pdf_mix = p*gampdf(x,a,b) + (1-p)*lognpdf(x,mu,sigma);

I am able to obtain the best fit model using mle, but I also want random numbers generated from this mixture distribution. Is this possible? Can I get some help on this?

R Venkatessh

Best Answer

Here's another method you might consider that would allow you to directly use the 'gamrnd' and 'lognrnd' functions in the Statistics Toolbox. Suppose you want an m by n matrix, R, of random values in accordance with your mixed distribution.

 U = rand(m,n)<=p; % U is true with probability p and false with probability 1-p
 R = U.*gamrnd(a,b,m,n)+(1-U).*lognrnd(mu,sigma,m,n);

R should have the desired distribution.

Related Solutions

MATLAB: Generate random numbers from a mixture distribution

Read David's answer. But let me explain it like this, because I think many people do not understand what a mixture distribution means or what it is.

A mixture distribution means you have two (well, or more) different distributions. I'll call them A and B. With probability p, a sample arises from distribution A, then with probability 1-p, the sample arises from distribution B.

The solution is simple. For each sample, first, choose a uniform random number. If the number is less than or equal to p, then you will sample from distribution A. If the number exceeds p, then you choose from distribution B. Easy, peasy.

Lets see how it might work. I'll pick two distributions that will be clearly different.

Distribution A: Uniform between limits [2,3]

Distribution B: Normally distributed, with mean 0, standard deviation 1.

Lets say 1000000 samples overall, enough to get a nice clean looking histogram. I'll set p as 0.4, arbitrarily. So roughly 40% of the samples will be uniform, 60% normal.

N = 1000000;
p = 0.4;
% U is a binary indicator variable, that tells how to
% sample for each sample. Here, 1 --> A, 0 --> B.
U = rand(N,1) <= p;
nA = sum(U);
nB = N - nA;
% preallocate X
X = zeros(N,1);
X(U) = rand(nA,1)*1 + 2;
X(~U) = randn(nB,1);
% finally, a histogram, just to show we did what was expected.
histogram(X,1000)

So we have some overlap between the distributions, but clearly a mixture of a Gaussian and a uniform, as we expected.

sum(U)
ans =
      399632

We would have expected roughly 400000 of the events to be from the uniform case. Pretty close.

MATLAB: How to go about finding the standard normal probability based on the z-score

doc normcdf
doc normpdf

When you know what you want but not sure the name, try something like

>> lookfor normal
realmin                        - Smallest positive normalized floating point number.
randn                          - Normally distributed pseudorandom numbers.
sprandn                        - Sparse normally distributed random matrix.
surfnorm                       - Surface normals.
isonormals                     - Isosurface normals.
cde                            - cd elliptic function with normalized complex argument.
sne                            - sn elliptic function with normalized complex argument.
addfreqcsmenu                  - Add a cs menu to switch between linear and normalized frequency
convertfrequnits               - converts between Normalized, Hz, kHz, etc
histfit                        - Histogram with superimposed fitted normal density.
jbtest                         - Jarque-Bera hypothesis test of composite normality.
lhsnorm                        - Generate a latin hypercube sample with a normal distribution
logncdf                        - Lognormal cumulative distribution function (cdf).
lognfit                        - Parameter estimates and confidence intervals for lognormal data.
logninv                        - Inverse of the lognormal cumulative distribution function (cdf).
lognlike                       - Negative log-likelihood for the lognormal distribution.
lognpdf                        - Lognormal probability density function (pdf).
lognrnd                        - Random arrays from the lognormal distribution.
lognstat                       - Mean and variance for the lognormal distribution.
mvncdf                         - Multivariate normal cumulative distribution function (cdf).
mvnpdf                         - Multivariate normal probability density function (pdf).
mvnrnd                         - Random vectors from the multivariate normal distribution.
normcdf                        - Normal cumulative distribution function (cdf).
normfit                        - Parameter estimates and confidence intervals for normal data.
norminv                        - Inverse of the normal cumulative distribution function (cdf).
normlike                       - Negative log-likelihood for the normal distribution.
normpdf                        - Normal probability density function (pdf).
normplot                       - Displays a normal probability plot.
normrnd                        - Random arrays from the normal distribution.
normspec                       - Plots normal density between specification limits.
normstat                       - Mean and variance for the normal distribution.
logn3fit                       - Fit a 3-param lognormal dist'n using cumulative probabilities.
wgtnormfit                     - Fitting example for a weighted normal distribution.
wgtnormfit2                    - Fitting example for a weighted normal distribution (log(sigma) parameterization).
>>

Judicious search terms help but seeing the list of things related to "normal" lets you find the two functions of interest (plus a lot more depending upon which toolboxes are available, maybe) that might be of use/interest...

Best Answer

Related Solutions

MATLAB: Generate random numbers from a mixture distribution

MATLAB: How to go about finding the standard normal probability based on the z-score

Related Question