entropy.estimate {vsgoftest}

Vasicek estimate of differential Shannon Entropy

Description

Computes Vasicek estimate of differential Shannon entropy from a numeric sample.

Usage

entropy.estimate(x,window)

Arguments

x

(numeric, vector) the numeric sample.

window

(numeric, single value) an integer between 1 and half on the sample size specifying the window size for computing Vasicek estimate. See Details for additional information.

Details

Vasicek estimator of Shannon entropy is defined, for a random sample X_1, \dots, X_n, by

\frac{1}{n}\sum_{i=1}^{n} \log (\frac{n}{2m}[X_{(i+m)}-X_{(i-m)}]),

where X_{(i)} is the order statistic, m<(n/2) is the window size, and X_{(i)}=X_{(1)} for i<1 and X_{(i)}=X_{(n)} for i>n.

Value

A single numeric value representing the Vasicek estimate of entropy of the sample

Author(s)

J. Lequesne [e-mail]

References

Vasicek, O., A test for normality based on sample entropy, Journal of the Royal Statistical Society, 38(1), 54-59 (1976).

See Also

vs.test which performs Vasicek-Song goodness-of-fit tests to the specified maximum entropy distribution family.

Examples

set.seed(2)
samp <- rnorm(100, mean = 0, s = 1)
entropy.estimate(x = samp, window = 8)
log(2*pi*exp(1))/2 #true value of entropy of normal distribution