lognfit
              Estimate parameters and confidence intervals for the log-normal distribution.
 paramhat = lognfit (x) returns the maximum likelihood
 estimates of the parameters of the log-normal distribution given the data in
 vector x.  paramhat([1, 2]) corresponds to the mean and
 standard deviation, respectively, of the associated normal distribution.
If a random variable follows this distribution, its logarithm is normally distributed with mean mu and standard deviation sigma.
 [paramhat, paramci] = lognfit (x) returns the 95%
 confidence intervals for the parameter estimates.
 […] = lognfit (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.
 […] = lognfit (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)).
 […] = lognfit (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)).
 […] = lognfit (…, 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
  With no censor, the estimate of the standard deviation,
 paramhat(2), is the square root of the unbiased estimate of the
 variance of log (x).  With censored data, the maximum
 likelihood estimate is returned.
Further information about the log-normal distribution can be found at https://en.wikipedia.org/wiki/Log-normal_distribution
See also: logncdf, logninv, lognpdf, lognrnd, lognlike, lognstat
Source Code: lognfit
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 ## Sample 3 populations from 3 different log-normal distibutions
 randn ("seed", 1);    # for reproducibility
 r1 = lognrnd (0, 0.25, 1000, 1);
 randn ("seed", 2);    # for reproducibility
 r2 = lognrnd (0, 0.5, 1000, 1);
 randn ("seed", 3);    # for reproducibility
 r3 = lognrnd (0, 1, 1000, 1);
 r = [r1, r2, r3];
 ## Plot them normalized and fix their colors
 hist (r, 30, 2);
 h = findobj (gca, "Type", "patch");
 set (h(1), "facecolor", "c");
 set (h(2), "facecolor", "g");
 set (h(3), "facecolor", "r");
 hold on
 ## Estimate their mu and sigma parameters
 mu_sigmaA = lognfit (r(:,1));
 mu_sigmaB = lognfit (r(:,2));
 mu_sigmaC = lognfit (r(:,3));
 ## Plot their estimated PDFs
 x = [0:0.1:6];
 y = lognpdf (x, mu_sigmaA(1), mu_sigmaA(2));
 plot (x, y, "-pr");
 y = lognpdf (x, mu_sigmaB(1), mu_sigmaB(2));
 plot (x, y, "-sg");
 y = lognpdf (x, mu_sigmaC(1), mu_sigmaC(2));
 plot (x, y, "-^c");
 ylim ([0, 2])
 xlim ([0, 6])
 hold off
 legend ({"Normalized HIST of sample 1 with mu=0, σ=0.25", ...
          "Normalized HIST of sample 2 with mu=0, σ=0.5", ...
          "Normalized HIST of sample 3 with mu=0, σ=1", ...
          sprintf("PDF for sample 1 with estimated mu=%0.2f and σ=%0.2f", ...
                  mu_sigmaA(1), mu_sigmaA(2)), ...
          sprintf("PDF for sample 2 with estimated mu=%0.2f and σ=%0.2f", ...
                  mu_sigmaB(1), mu_sigmaB(2)), ...
          sprintf("PDF for sample 3 with estimated mu=%0.2f and σ=%0.2f", ...
                  mu_sigmaC(1), mu_sigmaC(2))}, "location", "northeast")
 title ("Three population samples from different log-normal distibutions")
 hold off
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