Entropy
The information entropy of the wrapped normal distribution is defined as:
where is any interval of length . Defining and, the Jacobi triple product representation for the wrapped normal is:
where is the Euler function. The logarithm of the density of the wrapped normal distribution may be written:
Using the series expansion for the logarithm:
the logarithmic sums may be written as:
so that the logarithm of density of the wrapped normal distribution may be written as:
which is essentially a Fourier series in . Using the characteristic function representation for the wrapped normal distribution in the left side of the integral:
the entropy may be written:
which may be integrated to yield:
Read more about this topic: Wrapped Normal Distribution
Famous quotes containing the word entropy:
“Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.”
—Václav Havel (b. 1936)