hnfit
Estimate parameters and confidence intervals for the half-normal distribution.
paramhat = hnfit (x)
returns the maximum likelihood
estimates of the parameters of the half-normal distribution given the data in
vector x. paramhat(1)
is the location parameter,
mu, and paramhat(2)
is the scale parameter, sigma.
Although mu is returned in the estimated paramhat, hnfit
does not estimate the location parameter mu, and it must be assumed to
be known.
[paramhat, paramci] = hnfit (x, mu)
returns
the 95% confidence intervals for the estimated scale parameter sigma.
The first colummn of paramci includes the location parameter mu
without any confidence bounds.
[…] = hnfit (x, alpha)
also returns the
100 * (1 - alpha)
percent confidence intervals of the estimated
scale parameter. By default, the optional argument alpha is 0.05
corresponding to 95% confidence intervals.
The half-normal CDF is only defined for x >= mu
.
Further information about the half-normal distribution can be found at https://en.wikipedia.org/wiki/Half-normal_distribution
See also: hncdf, hninv, hnpdf, hnrnd, hnlike
Source Code: hnfit
## Sample 2 populations from different half-normal distibutions rand ("seed", 1); # for reproducibility r1 = hnrnd (0, 5, 5000, 1); rand ("seed", 2); # for reproducibility r2 = hnrnd (0, 2, 5000, 1); r = [r1, r2]; ## Plot them normalized and fix their colors hist (r, [0.5:20], 1); h = findobj (gca, "Type", "patch"); set (h(1), "facecolor", "c"); set (h(2), "facecolor", "g"); hold on ## Estimate their shape parameters mu_sigmaA = hnfit (r(:,1), 0); mu_sigmaB = hnfit (r(:,2), 0); ## Plot their estimated PDFs x = [0:0.2:10]; y = hnpdf (x, mu_sigmaA(1), mu_sigmaA(2)); plot (x, y, "-pr"); y = hnpdf (x, mu_sigmaB(1), mu_sigmaB(2)); plot (x, y, "-sg"); xlim ([0, 10]) ylim ([0, 0.5]) legend ({"Normalized HIST of sample 1 with μ=0 and σ=5", ... "Normalized HIST of sample 2 with μ=0 and σ=2", ... sprintf("PDF for sample 1 with estimated μ=%0.2f and σ=%0.2f", ... mu_sigmaA(1), mu_sigmaA(2)), ... sprintf("PDF for sample 2 with estimated μ=%0.2f and σ=%0.2f", ... mu_sigmaB(1), mu_sigmaB(2))}) title ("Two population samples from different half-normal distibutions") hold off |