MATLAB: Generate n samples of random variables based on a given discrete uniform distributions. Can anyone tell me what is the difference between the codes I wrote

Question

Question: Write a MATLAB program to sample K values from the probability mass function Pi=i/55, i=1, 2, ….10. Plot the histogram of generated values for K=50, 500, and 5000.

Version 1:

Best Answer

The first code generates one new random number each time through the loop, for a total of sampleK random numbers generated out of which sampleK random numbers are used.

The second code generates sampleK random numbers each time through the loop, and uses the i'th of them, ignorning the others, for a total of sampleK * sampleK random numbers generated out of which sampleK random numbers are used.

If you were to move the

u = rand(sampleK,1);

to before the for loop, then you would be making one call that generated sampleK random numbers all at one time, and then used one at a time. That would be more efficient than generating one random number sampleK times.

Related Solutions

MATLAB: Generate real random numbers

Such as randn() ? Or one of the random distribution tools in the Statistics Toolbox ?

MATLAB: Log likelihood for each distributions.

It's not clear to me what fails to match with what. These match:

>> x = -5*log(rand(100,1));
>> pd = fitdist(x,'weibull');
>> format compact
>> negloglik(pd)
ans =
  267.1545
>> sum(-log(pdf(pd,x)))
ans =
  267.1545
>> wbllike(pd.ParameterValues,x)
ans =
  267.1545

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Answer 1

The first code generates one new random number each time through the loop, for a total of sampleK random numbers generated out of which sampleK random numbers are used.

The second code generates sampleK random numbers each time through the loop, and uses the i'th of them, ignorning the others, for a total of sampleK * sampleK random numbers generated out of which sampleK random numbers are used.

If you were to move the

u = rand(sampleK,1);

to before the for loop, then you would be making one call that generated sampleK random numbers all at one time, and then used one at a time. That would be more efficient than generating one random number sampleK times.