How can i select random sample from mixture of two normal distributions in MATLAB ?

Hi everyone Could you please let me know how can i select random sample from contaminated normal distribution (i.e., mixture of two normal distributions) in MATLAB? .Suppose i need a sample of 100 values from mixture normal distributions such that 5% values are from Normal distribution with mean zero and variance 25 and 95% values are from normal with mean zero and variance 1. In mathematical terms i can write my problem as:

5% from N(0,25)+95% from N(0,1) This is mixture random sample of two normal distributions.

Answer 1

[Roger Stafford]

   r = rand(100,1)>=.05;
   R1 = normrnd(0,sqrt(25),100,1);
   R2 = normrnd(0,sqrt(1),100,1);
   S = (1-r).*R1+r.*R2;

S contains your 100 samples.

This assumes that your two normal distributions are statistically independent.

[zahid]

Dear Roger Stafford When i run r = rand(100,1)>=.05;it gives mean a vector having four zeros and 96, ones.Logically it should give me 5 zeros and 95 ones.What is wrong with it?Suppose i change to 20% samples from one distribution and and 80% sample from another then it will deal .Please generalized this random selection to any percentage that i want.

[Roger Stafford]

_“When i run r = rand(100,1)>=.05;it gives mean a vector having four zeros and 96 ones.“_

That is NOT how ‘rand’ works, Zahid. The ‘rand’ function is statistically uniform throughout the range from 0 to 1. That means, statistically speaking, there is a 5%, that is 1 in 20, chance that its value will lie between 0 and .05 and 19 out of 20 chance that it will lie outside that range. You can arrive at that conclusion by dividing .05-0 by 1 to get .05 = 1/20, and dividing 1-.05 by 1 to get .95 = 19/20. It is a very simple calculation.

You cannot conclude that out of each 100 samples there will be four zeros or five zeros or any other definite number. We are dealing with a statistical situation here. All you can say is that the average number would be five zeros and ninety-five ones. That is all you can say.

[zahid]

Dear Stafford Thank you very much for your explanation.Logically i taking 5% values from one distribtuion i.e 5 values out of 100 as sample size is 100.Similarly 95% values from other normal distribution which means 95 values out of 100.How can i do this?Your logic i did not understand

[zahid]

Thank your Roger Stafford now i have get your point.The logic which you are using is true in probability sense.

Regards