Statistics: unidfit

### 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