Probabilities.ZipfPDF Method

Overload List

#	Signature	Description
1	procedure ZipfPDF(const X: TMtxVecInt; s: Double; N: Integer; const Res: TDenseMtxVec);	Zipf distribution PDF (vectorized).
2	function ZipfPDF(x: Integer; s: Double; N: Integer): Double;	Zipf (finite/truncated) probability mass function (PMF).

Zipf distribution PDF (vectorized).

#	Name	Description
1	X	Defines distribution domain, real vector or matrix with integer values on interval [1,Inf).
2	s	Distribution parameter, real positive value.
3	N	Distribution parameter, positive integer.
4	Res	After calculation stores the PDF calculated from X,s and N. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.

Result: stored in self (calling object)

Zipf (finite/truncated) probability mass function (PMF).

#	Name	Description
1	x	Function domain, positive integer on the closed interval [1,N].
2	s	Exponent (shape) parameter, real positive value.
3	N	Number of elements (support upper bound), positive integer.

Returns: Double - the finite Zipf probability mass function (PMF) at x using parameters s and N. Returns NAN when s<=0, N<=0, or x outside [1,N].

Remarks:

Computes the finite (truncated) Zipf PMF over the rank support 1,...,N:

PMF(x| s,N)=(1/x^s)/H(N,s), H(N,s)=sum_(k=1)^N1/k^s

where $H(N,s)$ is the generalized harmonic number. Domain: x in {1,...,N}, s>0, N>0; otherwise the result is NaN.

See Also: Probabilities.ZipfCDF, Probabilities.ZipfCDFInv