Function Reference: geofit

statistics: pshat = geofit (x)
statistics: [pshat, psci] = geofit (x)
statistics: [pshat, psci] = geofit (x, alpha)
statistics: [pshat, psci] = geofit (x, alpha, freq)

Estimate parameter and confidence intervals for the geometric distribution.

pshat = geofit (x) returns the maximum likelihood estimate (MLE) of the probability of success for the geometric distribution. x must be a vector.

[pshat, psci] = geofit (x, 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. Pass in [] for alpha to use the default values.

[…] = geofit (x, alpha, freq) accepts a frequency vector, freq, of the same size as x. freq typically contains integer frequencies for the corresponding elements in x, but it can contain any non-integer non-negative values. By default, or if left empty, freq = ones (size (x)).

The geometric distribution models the number of failures (x) of a Bernoulli trial with probability ps before the first success.

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

See also: geocdf, geoinv, geopdf, geornd, geostat

Source Code: geofit

Example: 1

  

 ## Sample 2 populations from different geometric distibutions
 rande ("seed", 1);    # for reproducibility
 r1 = geornd (0.15, 1000, 1);
 rande ("seed", 2);    # for reproducibility
 r2 = geornd (0.5, 1000, 1);
 r = [r1, r2];

 ## Plot them normalized and fix their colors
 hist (r, 0:0.5:20.5, 1);
 h = findobj (gca, "Type", "patch");
 set (h(1), "facecolor", "c");
 set (h(2), "facecolor", "g");
 hold on

 ## Estimate their probability of success
 pshatA = geofit (r(:,1));
 pshatB = geofit (r(:,2));

 ## Plot their estimated PDFs
 x = [0:15];
 y = geopdf (x, pshatA);
 plot (x, y, "-pg");
 y = geopdf (x, pshatB);
 plot (x, y, "-sc");
 xlim ([0, 15])
 ylim ([0, 0.6])
 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 geometric distibutions")
 hold off
plotted figure