invgfit
              Estimate mean and confidence intervals for the inverse Gaussian distribution.
 mu0 = invgfit (x) returns the maximum likelihood
 estimates of the parameters of the inverse Gaussian distribution given the
 data in x.  paramhat(1) is the scale parameter, mu,
 and paramhat(2) is the shape parameter, lambda.
 [paramhat, paramci] = invgfit (x) returns the 95%
 confidence intervals for the parameter estimates.
 […] = invgfit (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.
 […] = invgfit (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)).
 […] = invgfit (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)).
 […] = invgfit (…, 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 inverse Gaussian distribution can be found at https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution
See also: invgcdf, invginv, invgpdf, invgrnd, invglike, invgstat
Source Code: invgfit
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 ## Sample 3 populations from different inverse Gaussian distibutions
 rand ("seed", 5); randn ("seed", 5);   # for reproducibility
 r1 = invgrnd (1, 0.2, 2000, 1);
 rand ("seed", 2); randn ("seed", 2);   # for reproducibility
 r2 = invgrnd (1, 3, 2000, 1);
 rand ("seed", 7); randn ("seed", 7);   # for reproducibility
 r3 = invgrnd (3, 1, 2000, 1);
 r = [r1, r2, r3];
 ## Plot them normalized and fix their colors
 hist (r, [0.1:0.1:3.2], 9);
 h = findobj (gca, "Type", "patch");
 set (h(1), "facecolor", "c");
 set (h(2), "facecolor", "g");
 set (h(3), "facecolor", "r");
 ylim ([0, 3]);
 xlim ([0, 3]);
 hold on
 ## Estimate their MU and LAMBDA parameters
 mu_lambdaA = invgfit (r(:,1));
 mu_lambdaB = invgfit (r(:,2));
 mu_lambdaC = invgfit (r(:,3));
 ## Plot their estimated PDFs
 x = [0:0.1:3];
 y = invgpdf (x, mu_lambdaA(1), mu_lambdaA(2));
 plot (x, y, "-pr");
 y = invgpdf (x, mu_lambdaB(1), mu_lambdaB(2));
 plot (x, y, "-sg");
 y = invgpdf (x, mu_lambdaC(1), mu_lambdaC(2));
 plot (x, y, "-^c");
 hold off
 legend ({"Normalized HIST of sample 1 with μ=1 and λ=0.5", ...
          "Normalized HIST of sample 2 with μ=2 and λ=0.3", ...
          "Normalized HIST of sample 3 with μ=4 and λ=0.5", ...
          sprintf("PDF for sample 1 with estimated μ=%0.2f and λ=%0.2f", ...
                  mu_lambdaA(1), mu_lambdaA(2)), ...
          sprintf("PDF for sample 2 with estimated μ=%0.2f and λ=%0.2f", ...
                  mu_lambdaB(1), mu_lambdaB(2)), ...
          sprintf("PDF for sample 3 with estimated μ=%0.2f and λ=%0.2f", ...
                  mu_lambdaC(1), mu_lambdaC(2))})
 title ("Three population samples from different inverse Gaussian distibutions")
 hold off
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