Categories &

Functions List

Function Reference: binofit

statistics: pshat = binofit (x, n)
statistics: [pshat, psci] = binofit (x, n)
statistics: [pshat, psci] = binofit (x, n, alpha)

Estimate parameter and confidence intervals for the binomial distribution.

pshat = binofit (x, n) returns the maximum likelihood estimate (MLE) of the probability of success for the binomial distribution. x and n are scalars containing the number of successes and the number of trials, respectively. If x and n are vectors, binofit returns a vector of estimates whose i-th element is the parameter estimate for x(i) and n(i). A scalar value for x or n is expanded to the same size as the other input.

[pshat, psci] = binofit (x, n, alpha) also returns the 100 * (1 - alpha) percent confidence intervals of the estimated parameter. By default, the optional argument alpha is 0.05 corresponding to 95% confidence intervals.

binofit treats a vector x as a collection of measurements from separate samples, and returns a vector of estimates. If you want to treat x as a single sample and compute a single parameter estimate and confidence interval, use binofit (sum (x), sum (n)) when n is a vector, and binofit (sum (x), n * length (x)) when n is a scalar.

Further information about the binomial distribution can be found at https://en.wikipedia.org/wiki/Binomial_distribution

See also: binocdf, binoinv, binopdf, binornd, binolike, binostat

Source Code: binofit

Example: 1

Sample 2 populations from different binomial distributions

 rand ('seed', 1);    # for reproducibility
 r1 = binornd (50, 0.15, 1000, 1);
 rand ('seed', 2);    # for reproducibility
 r2 = binornd (100, 0.5, 1000, 1);
 r = [r1, r2];

Plot them normalized and fix their colors

 hist (r, 23, 0.35);
 h = findobj (gca, 'Type', 'patch');
 set (h(1), 'facecolor', 'c');
 set (h(2), 'facecolor', 'g');
 hold on

Estimate their probability of success

 pshatA = binofit (r(:,1), 50);
 pshatB = binofit (r(:,2), 100);

Plot their estimated PDFs

 x = [min(r(:,1)):max(r(:,1))];
 y = binopdf (x, 50, mean (pshatA));
 plot (x, y, '-pg');
 x = [min(r(:,2)):max(r(:,2))];
 y = binopdf (x, 100, mean (pshatB));
 plot (x, y, '-sc');
 ylim ([0, 0.2])
 legend ({'Normalized HIST of sample 1 with ps=0.15', ...
          'Normalized HIST of sample 2 with ps=0.50', ...
          sprintf("PDF for sample 1 with estimated ps=%0.2f", ...
                  mean (pshatA)), ...
          sprintf("PDF for sample 2 with estimated ps=%0.2f", ...
                  mean (pshatB))})
 title ('Two population samples from different binomial distributions')
 hold off
plotted figure