Function Reference: unidfit

statistics: Nhat = unidfit (x)
statistics: [Nhat, Nci] = unidfit (x)
statistics: [Nhat, Nci] = unidfit (x, alpha)
statistics: [Nhat, Nci] = unidfit (x, alpha, freq)

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

Example: 1

  

 ## 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
plotted figure