Does anyone know how to create a custom distribution?

the thing is, i want to define a custom distribution in statistic toolbox,the custom distribution is like this pdf = (1-p)*normalpdf +p*exppdf, it's a combination of two distribution.

there is an example from matlab,it's laplace distrbution, but i want a combination of two distributions.it's hard for me . Could someone give me an idea ?

Answer 1

[Image Analyst]

Try this link: http://www.mathworks.com/matlabcentral/fileexchange/7309-randraw. It has numerous distributions, along with source code so you can see how it's done.

Answer 2

[Tom Lane]

You have a four-parameter distribution with density

(1-p)*normpdf(x,mu,sigma) + p*exppdf(x,lambda)

and with a cdf that is similarly a linear combination of normcdf and expcdf. You can generate random numbers from it by take the normal value with probability (1-p) and the exponential value with probability p. The inversecdf is trickier but you might find fzero to be helpful:

>> p = .6; mu = 0; sigma = 1; lambda = 3;
>> mycdf = @(x) (1-p)*normcdf(x,mu,sigma) + p*expcdf(x,lambda);
>> mycdf(1.5)
ans =
    0.6094
>> fzero(@(y) mycdf(y)-.6094,1)
ans =
    1.5002

[jeff himmel]

http://www.mathworks.de/matlabcentral/answers/15734-custom-distribution-in-distribution-fitting-tool I coded the mixture of two normal distributions(it looks easy.) and then import it to the dfittoo. But I have the same problem like this http://www.mathworks.de/matlabcentral/answers/15734-custom-distribution-in-distribution-fitting-tool Can you help me?