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Function Reference: bisafit

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

Estimate mean and confidence intervals for the Birnbaum-Saunders distribution.

muhat = bisafit (x) returns the maximum likelihood estimates of the parameters of the Birnbaum-Saunders distribution given the data in x. paramhat(1) is the scale parameter, beta, and paramhat(2) is the shape parameter, gamma.

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

[…] = bisafit (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.

[…] = bisafit (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)).

[…] = bisafit (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)).

[…] = bisafit (…, options) specifies control parameters for the iterative algorithm used to compute ML estimates with the fminsearch function. options is a structure with the following fields and their default values:

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

Further information about the Birnbaum-Saunders distribution can be found at https://en.wikipedia.org/wiki/Birnbaum%E2%80%93Saunders_distribution

See also: bisacdf, bisainv, bisapdf, bisarnd, bisalike, bisastat

Source Code: bisafit

Example: 1

  

 ## Sample 3 populations from different Birnbaum-Saunders distibutions
 rand ("seed", 5);    # for reproducibility
 r1 = bisarnd (1, 0.5, 2000, 1);
 rand ("seed", 2);    # for reproducibility
 r2 = bisarnd (2, 0.3, 2000, 1);
 rand ("seed", 7);    # for reproducibility
 r3 = bisarnd (4, 0.5, 2000, 1);
 r = [r1, r2, r3];

 ## Plot them normalized and fix their colors
 hist (r, 80, 4.2);
 h = findobj (gca, "Type", "patch");
 set (h(1), "facecolor", "c");
 set (h(2), "facecolor", "g");
 set (h(3), "facecolor", "r");
 ylim ([0, 1.1]);
 xlim ([0, 8]);
 hold on

 ## Estimate their α and β parameters
 beta_gammaA = bisafit (r(:,1));
 beta_gammaB = bisafit (r(:,2));
 beta_gammaC = bisafit (r(:,3));

 ## Plot their estimated PDFs
 x = [0:0.1:8];
 y = bisapdf (x, beta_gammaA(1), beta_gammaA(2));
 plot (x, y, "-pr");
 y = bisapdf (x, beta_gammaB(1), beta_gammaB(2));
 plot (x, y, "-sg");
 y = bisapdf (x, beta_gammaC(1), beta_gammaC(2));
 plot (x, y, "-^c");
 hold off
 legend ({"Normalized HIST of sample 1 with β=1 and γ=0.5", ...
          "Normalized HIST of sample 2 with β=2 and γ=0.3", ...
          "Normalized HIST of sample 3 with β=4 and γ=0.5", ...
          sprintf("PDF for sample 1 with estimated β=%0.2f and γ=%0.2f", ...
                  beta_gammaA(1), beta_gammaA(2)), ...
          sprintf("PDF for sample 2 with estimated β=%0.2f and γ=%0.2f", ...
                  beta_gammaB(1), beta_gammaB(2)), ...
          sprintf("PDF for sample 3 with estimated β=%0.2f and γ=%0.2f", ...
                  beta_gammaC(1), beta_gammaC(2))})
 title ("Three population samples from different Birnbaum-Saunders distibutions")
 hold off
plotted figure