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
## 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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