Function Reference: lognfit

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

Estimate parameters and confidence intervals for the lognormal distribution.

paramhat = lognfit (x) returns the maximum likelihood estimates of the parameters of the lognormal 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 lognormal distribution can be found at https://en.wikipedia.org/wiki/Log-normal_distribution

See also: logncdf, logninv, lognpdf, lognrnd, lognlike, lognstat

Source Code: lognfit

Example: 1

  

 ## 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
plotted figure