Categories &

Functions List

Function Reference: unifit

statistics: ahat = unifit (x)
statistics: [ahat, bhat] = unifit (x)
statistics: [ahat, bhat, aci, bci] = unifit (x)
statistics: […] = unifit (x, alpha)
statistics: […] = unifit (x, alpha, freq)

Estimate parameters and confidence intervals for the continuous uniform distribution.

[ahat, bhat] = unifit (x) returns the maximum likelihood estimates of the lower and upper endpoints, a and b, of the continuous uniform distribution given the data in x. Each estimate is returned as a separate output.

x may be a vector, which is fitted as a single sample, or a matrix, which is fitted column by column. For a matrix of n columns ahat and bhat are 1-by-n row vectors and aci and bci are 2-by-n.

[ahat, bhat, aci, bci] = unifit (x) also returns the 95% confidence intervals of the two estimates, one column per column of x, with the lower bound in the first row and the upper bound in the second. ahat is the upper bound of aci and bhat the lower bound of bci, since no sample can fall outside the fitted range.

[…] = unifit (x, alpha) also returns the 100 * (1 - alpha) percent confidence intervals of the estimated parameters. By default, the optional argument alpha is 0.05 corresponding to 95% confidence intervals. Pass in [] for alpha to use the default values.

[…] = unifit (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)). This third argument is an Octave extension; MATLAB’s unifit takes two inputs at most, and freq is accepted for a vector x only.

Further information about the continuous uniform distribution can be found at https://en.wikipedia.org/wiki/Continuous_uniform_distribution

See also: unifcdf, unifinv, unifpdf, unifrnd, unifstat

Source Code: unifit

Sample 2 populations from different continuous uniform distributions

 rand ('seed', 5);    # for reproducibility
 r1 = unifrnd (2, 5, 2000, 1);
 rand ('seed', 6);    # for reproducibility
 r2 = unifrnd (3, 9, 2000, 1);
 r = [r1, r2];

Plot them normalized and fix their colors

 hist (r, 0:0.5:10, 2);
 h = findobj (gca, 'Type', 'patch');
 set (h(1), 'facecolor', 'c');
 set (h(2), 'facecolor', 'g');
 hold on

Estimate their probability of success

 a_bA = unifit (r(:,1));
 a_bB = unifit (r(:,2));

Plot their estimated PDFs

 x = [0:10];
plotted figure 

 y = unifpdf (x, a_bA(1), a_bA(2));
error: a_bA(2): out of bound 1 (dimensions are 1x1)
 plot (x, y, '-pg');
 y = unifpdf (x, a_bB(1), a_bB(2));
 plot (x, y, '-sc');
 xlim ([1, 10])
 ylim ([0, 0.5])
 legend ({'Normalized HIST of sample 1 with a=2 and b=5', ...
          'Normalized HIST of sample 2 with a=3 and b=9', ...
          sprintf("PDF for sample 1 with estimated a=%0.2f and b=%0.2f", ...
                  a_bA(1), a_bA(2)), ...
          sprintf("PDF for sample 2 with estimated a=%0.2f and b=%0.2f", ...
                  a_bB(1), a_bB(2))})
 title ('Two population samples from different continuous uniform distributions')
 hold off