CentralAndStandardizedStatistics: Compute central and standardized statistics.

In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.

Description

Compute central and standardized statistics, as described in A. Meucci "Risk and Asset Allocation", Springer, 2005.

Computes the central moments

CM_1^X \equiv μ_{X}\,, \quad CM_n^X \equiv E \{(X - E\{ X \})^{n}\}\,, \quad n=2,3,… ,

and from them the standarized statistics

μ_{X},σ_{X},sk_{X},ku_{X},γ_{X}^{(5)}, … ,γ_{X}^{(n)} .

where

γ_{X}^{(n)} \equiv E \{(X - μ_{X})^{n}\}/σ_{X}^{n},\quad n≥q3 .

Usage

  CentralAndStandardizedStatistics(X, N)

Arguments

X	[vector] (J x 1) draws from the distribution
N	[scalar] highest degree for the central moment

Value

ga [vector] (1 x N) standardized statistics up to order N

mu [vector] (1 x N) central moments up to order N

Author(s)

Xavier Valls [e-mail]

References

A. Meucci - "Exercises in Advanced Risk and Portfolio Management" http://symmys.com/node/170, "E 97 - Projection of skewness, kurtosis, and all standardized summary statistics". See Meucci's script for "CentralAndStandardizedStatistics.m"

Kendall, M., Stuart, A. - "The Advanced Theory of Statistics", 1969. Volume, 3rd Edition. Griffin.

A. Meucci - "Annualization and general projection of skweness, kurtosis, and all summary statistics", GARP Risk Professional August 2010, 55-56. http://symmys.com/node/136.

R-Finance/Meucci documentation built on May 8, 2019, 3:52 a.m.