bisafit
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
## 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
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