Description Usage Arguments Details Value Examples
View source: R/moezipfR.moments.R
General function to compute the k-th moment of the distribution, for any k ≥q 1 when it exists. Note that the k-th moment exists if and only if α > k + 1. When k = 1, this function returns the same value as the moezipfR.mean function.
1 | moezipfR.moments(k, alpha, beta, tolerance = 10^(-4))
|
k |
Order of the moment to compute. |
alpha |
Value of the α parameter (α > k + 1). |
beta |
Value of the β parameter (β > 0). |
tolerance |
Tolerance used in the calculations (default = 10^{-4}). |
The k-th moment of the MOEZipf distribution is finite for α values strictly greater than k + 1. For a random variable Y that follows a MOEZipf distribution with parameters α and β, the k-th moment is computed as:
E(Y^k) = ∑_{x = 1} ^∞ \frac{β ζ(α) x^{-α + k}}{[ζ(α) - \bar{β}ζ(α, x)][ζ(α) - \bar{β}ζ(α, x + 1)]}\,, α ≥q k + 1\,, β > 0
The k-th moment is computed calculating the partial sums of the serie, and it stops when two
consecutive partial sums differs less than the tolerance
value.
The last partial sum is returned.
A positive real value corresponding to the k-th moment of the distribution.
1 2 | moezipfR.moments(3, 4.5, 1.3)
moezipfR.moments(3, 4.5, 1.3, 1*10^(-3))
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.