Question

I need to calculate the probability mass function, and cumulative distribution function, of the binomial distribution. I would like to use MATLAB to do this (raw MATLAB, no toolboxes). I can calculate these myself, but was hoping to use a predefined function and can t find any. Is there something out there?

function x = homebrew_binomial_pmf(N,p)
    x = [1];
    for i = 1:N
       x = [0 x]*p + [x 0]*(1-p);
    end

Answer 1

You can use the function NCHOOSEK to compute the binomial coefficient. With that, you can create a function that computes the value of the probability mass function for a set of k values for a given N and p:

function pmf = binom_dist(N,p,k)
  nValues = numel(k);
  pmf = zeros(1,nValues);
  for i = 1:nValues
    pmf(i) = nchoosek(N,k(i))*p^k(i)*(1-p)^(N-k(i));
  end
end

To plot the probability mass function, you would do the following:

k = 0:40;
pmf = binom_dist(40,0.5,k);
plot(k,pmf, r. );

and the cumulative distribution function can be found from the probability mass function using CUMSUM:

cummDist = cumsum(pmf);
plot(k,cummDist, r. );

NOTE: When the binomial coefficient returned from NCHOOSEK is large you can end up losing precision. A very nice alternative is to use the submission Variable Precision Integer Arithmetic from John D Errico on the MathWorks File Exchange. By converting your numbers to his vpi type, you can avoid the precision loss.

Answer 2

octave provides a good collection of distribution pdf, cdf, quantile; they have to be translated from octave, but this is relatively trivial (convert endif to end, convert != to ~=, etc;) see e.g. octave binocdf for the binomial cdf function.

Answer 3

looks like for the CDF of the binomial distribution, my best bet is the incomplete beta function betainc.

Answer 4

For PDF

x=1:15
p=.45

c=binopdf(x,15,p)

plot(x,c)

Similarly CDF

D=binocdf(x,15,p) 

plot(x,D)

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