Enq: Grassberger's expectation of n^q

In entropart: Entropy Partitioning to Measure Diversity

Grassberger's expectation of n^q

Description

Expected value of n^q when n follows a Poisson law.

Usage

Enq(n, q)

Arguments

n	A positive integer vector.
q	A positive number.

Details

The expectation of n^q when n follows a Poisson ditribution has been derived by Grassberger (1988).

Value

A vector of the same length as n containing the transformed values.

Note

The function is computed using the beta.function.

Its value is 0 for n-q+1<0.

References

Grassberger, P. (1988). Finite sample corrections to entropy and dimension estimates. Physics Letters A 128(6-7): 369-373.

Examples

# Compare
n <- c(2,3)
Enq(n, q=2)
# with
n^2

# Result is 1
Enq(n, q=0)
# Result is 0
Enq(n, q=5)

entropart documentation built on Sept. 11, 2024, 6:20 p.m.