unidfit
              Estimate parameter and confidence intervals for the discrete uniform distribution.
 Nhat = unidfit (x) returns the maximum likelihood estimate
 (MLE) of the maximum observable value for the discrete uniform distribution.
 x must be a vector.
 [Nhat, Nci] = unidfit (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.
 […] = unidfit (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)).
Further information about the discrete uniform distribution can be found at https://en.wikipedia.org/wiki/Discrete_uniform_distribution
See also: unidcdf, unidinv, unidpdf, unidrnd, unidstat
Source Code: unidfit
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 ## Sample 2 populations from different discrete uniform distibutions
 rand ("seed", 1);    # for reproducibility
 r1 = unidrnd (5, 1000, 1);
 rand ("seed", 2);    # for reproducibility
 r2 = unidrnd (9, 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
 NhatA = unidfit (r(:,1));
 NhatB = unidfit (r(:,2));
 ## Plot their estimated PDFs
 x = [0:10];
 y = unidpdf (x, NhatA);
 plot (x, y, "-pg");
 y = unidpdf (x, NhatB);
 plot (x, y, "-sc");
 xlim ([0, 10])
 ylim ([0, 0.4])
 legend ({"Normalized HIST of sample 1 with N=5", ...
          "Normalized HIST of sample 2 with N=9", ...
          sprintf("PDF for sample 1 with estimated N=%0.2f", NhatA), ...
          sprintf("PDF for sample 2 with estimated N=%0.2f", NhatB)})
 title ("Two population samples from different discrete uniform distibutions")
 hold off
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