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Function Reference: wblfit

statistics: paramhat = wblfit (x)
statistics: [paramhat, paramci] = wblfit (x)
statistics: [paramhat, paramci] = wblfit (x, alpha)
statistics: […] = wblfit (x, alpha, censor)
statistics: […] = wblfit (x, alpha, censor, freq)
statistics: […] = wblfit (x, alpha, censor, freq, options)

Estimate parameters and confidence intervals for the Weibull distribution.

muhat = wblfit (x) returns the maximum likelihood estimates of the parameters of the Weibull distribution given the data in x. paramhat(1) is the scale parameter, lambda, and paramhat(2) is the shape parameter, k.

[paramhat, paramci] = wblfit (x) returns the 95% confidence intervals for the parameter estimates.

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

[…] = wblfit (x, alpha, censor) accepts a boolean vector, censor, of the same size as x with 1s for observations that are right-censored and 0s for observations that are observed exactly. By default, or if left empty, censor = zeros (size (x)).

[…] = wblfit (x, alpha, censor, 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)).

[…] = wblfit (…, options) specifies control parameters for the iterative algorithm used to compute the maximum likelihood estimates. options is a structure with the following field and its default value:

  • options.Display = "off"
  • options.MaxFunEvals = 400
  • options.MaxIter = 200
  • options.TolX = 1e-6

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

The prob.WeibullDistribution class names these same two parameters A and B, after MATLAB. lambda is its A and k is its B.

See also: wblcdf, wblinv, wblpdf, wblrnd, wbllike, wblstat

Source Code: wblfit

Sample 3 populations from 3 different Weibull distributions

 rande ('state', 42);
 r1 = wblrnd (2, 4, 2000, 1);
 r2 = wblrnd (5, 2, 2000, 1);
 r3 = wblrnd (1, 5, 2000, 1);
 r = [r1, r2, r3];

Plot them normalized and fix their colors

 hist (r, 30, [2.5 2.1 3.2]);
 h = findobj (gca, 'Type', 'patch');
 set (h(1), 'facecolor', 'c');
 set (h(2), 'facecolor', 'g');
 set (h(3), 'facecolor', 'r');
 ylim ([0, 2]);
 xlim ([0, 10]);
 hold on

Estimate their lambda parameter

 lambda_kA = wblfit (r(:,1));
 lambda_kB = wblfit (r(:,2));
 lambda_kC = wblfit (r(:,3));

Plot their estimated PDFs

 x = [0:0.1:15];
 y = wblpdf (x, lambda_kA(1), lambda_kA(2));
 plot (x, y, '-pr');
 y = wblpdf (x, lambda_kB(1), lambda_kB(2));
 plot (x, y, '-sg');
 y = wblpdf (x, lambda_kC(1), lambda_kC(2));
 plot (x, y, '-^c');
 hold off
 legend ({'Normalized HIST of sample 1 with λ=2 and k=4', ...
          'Normalized HIST of sample 2 with λ=5 and k=2', ...
          'Normalized HIST of sample 3 with λ=1 and k=5', ...
          sprintf("PDF for sample 1 with estimated λ=%0.2f and k=%0.2f", ...
                  lambda_kA(1), lambda_kA(2)), ...
          sprintf("PDF for sample 2 with estimated λ=%0.2f and k=%0.2f", ...
                  lambda_kB(1), lambda_kB(2)), ...
          sprintf("PDF for sample 3 with estimated λ=%0.2f and k=%0.2f", ...
                  lambda_kC(1), lambda_kC(2))})
 title ('Three population samples from different Weibull distributions')
 hold off
plotted figure