expfit
Estimate mean and confidence intervals for the exponential distribution.
muhat = expfit (x) returns the maximum likelihood estimate
of the mean parameter, muhat, of the exponential distribution given the
data in x. x is expected to be a non-negative vector. If x
is an array, the mean will be computed for each column of x. If any
elements of x are NaN, that vector’s mean will be returned as NaN.
[muhat, muci] = expfit (x) returns the 95%
confidence intervals for the parameter estimate. If x is a vector,
muci is a two element column vector. If x is an array, each
column of data will have a confidence interval returned as a two-row array.
[…] = evfit (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. Any invalid values for alpha
will return NaN for both CI bounds.
[…] = expfit (x, alpha, censor) accepts a
logical or numeric array, censor, of the same size as x with
1s for observations that are right-censored and 0s for
observations that are observed exactly. Any non-zero elements are regarded
as 1s. By default, or if left empty,
censor = zeros (size (x)).
[…] = expfit (x, alpha, censor, freq)
accepts a frequency array, 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)).
Matlab incompatibility: Matlab’s expfit produces unpredictable results
for some cases with higher dimensions (specifically 1 x m x n x ... arrays).
Octave’s implementation allows for arrays, consistently performing
calculations on individual column vectors. Additionally, censor and
freq can be used with arrays of any size, whereas Matlab only allows
their use when x is a vector.
A common alternative parameterization of the exponential distribution is to use the parameter defined as the mean number of events in an interval as opposed to the parameter , which is the mean wait time for an event to occur. and are reciprocals, i.e. .
Further information about the exponential distribution can be found at https://en.wikipedia.org/wiki/Exponential_distribution
See also: expcdf, expinv, explpdf, exprnd, explike, expstat
Source Code: expfit
## Sample 3 populations from 3 different exponential distibutions
rande ("seed", 1); # for reproducibility
r1 = exprnd (2, 4000, 1);
rande ("seed", 2); # for reproducibility
r2 = exprnd (5, 4000, 1);
rande ("seed", 3); # for reproducibility
r3 = exprnd (12, 4000, 1);
r = [r1, r2, r3];
## Plot them normalized and fix their colors
hist (r, 48, 0.52);
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 parameter
muhat = expfit (r);
## Plot their estimated PDFs
x = [0:max(r(:))];
y = exppdf (x, muhat(1));
plot (x, y, "-pr");
y = exppdf (x, muhat(2));
plot (x, y, "-sg");
y = exppdf (x, muhat(3));
plot (x, y, "-^c");
ylim ([0, 0.6])
xlim ([0, 40])
legend ({"Normalized HIST of sample 1 with μ=2", ...
"Normalized HIST of sample 2 with μ=5", ...
"Normalized HIST of sample 3 with μ=12", ...
sprintf("PDF for sample 1 with estimated μ=%0.2f", muhat(1)), ...
sprintf("PDF for sample 2 with estimated μ=%0.2f", muhat(2)), ...
sprintf("PDF for sample 3 with estimated μ=%0.2f", muhat(3))})
title ("Three population samples from different exponential distibutions")
hold off
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