How do I combine two different distributions in MATLAB?

Suppose I have X ~ Norm(x,y) and Y ~ Exponential(k)

I wish to create a new variable T = X + Y. How would this be done?

I need to be able to generate random numbers from the new variable T. Say I want to generate 1000 values how would I now do this?

Any help greatly appreciated.

Thanks.

Answer 1

[José-Luis]

your_fun = @(average,var,k,numRows,numCols) average + var.*randn(numRows,numCols) + exprnd(k,numRows,numCols)

And to get values:

 your_vals = your_fun(3,2,5,10,10)

will give you a 10 x 10 matrix of random values.

[Javier]

Hello José

Can you please prove the source of you answer (book, paper or link).

Im just curious

Thanks in advance

[James Newton]

He's just defining a function which takes as its arguments, the parameters of the two distributions.

So for a normal distribution you have your "average" and "variance" and for an exponential distribution you have your lambda value which is "k" in this instance.

I'm just a little confused about why he did average + var.*randn(etc. etc.) though.

[Daniel Shub]

@Javier where are you confused? Are you confused that mu + (sigma.^2).*randn generates a random numbers with a Gaussian distribution with mean mu and standard deviation sigma?

[José-Luis]

Well, I am sure there is an original paper defining the normal distribution, probably by Gauss, but any statistics book will give you the functions for both distributions. What James wanted was a random variable that is the sum of two other random variables. If you are talking about how the values are sampled, the default in Matlab is based on the Mersenne-Twister algorithm:

Matsumoto, M.; Nishimura, T. (1998). "Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator". ACM Transactions on Modeling and Computer Simulation 8 (1): 3–30. doi:10.1145/272991.272995

The rest is just a more or less forward application of the formula (M-T will give you a value that you translate into a quantile that you then use to get your random value, using the formula that defines it).

[Daniel Shub]

@James, he could have done normrnd(mu,sigma,m,n), but it would be a hair slower because of the extra error checking.

Answer 2

[James Newton]

Thanks for the answer, it makes sense, forgot about making a function!

[José-Luis]

My pleasure.