one_combination: Generate symbolic expression for expectation

Description Usage Arguments Details Value Examples

View source: R/expectStr.R

Description

Generate a string with symbolic expression for expectation of powers and products of non-central (raw) sample moments of an arbitrary order.

Usage

1
one_combination(powvect, smpsize = "n")

Arguments

powvect

vector of j[1], ..., j[m] (see "Details") of exponents for non-central moments. The index of an element of this vector indicates a corresponding order, e.g. for E(X-bar^5 X^4), powvect = c(5, 0, 0, 1). Thus the vector will have m elements if m is the highest order.

smpsize

symbol to be used for sample size.

Details

For a zero-mean random variable X and a sample X[1], ..., X[n], find E(X-bar^{j_1} {X^2}-bar^{j[2]} \cdots {X^m}-bar^{j[m]}), where {X^k}-bar = sum_{i = 1}^n X[i]^k is a k'th non-central sample moment. The expression is given in terms of sample size and true moments μ[k] of X. These expectations can subsequently be used for generating unbiased central moment estimators of an arbitrary order, Edgeworth expansions, and possibly solving other higher-order problems.

Value

A string representing a symbolic expression for further processing using computer algebra (e.g. with Sage or SymPy), for calculating numeric values, or to be rendered with Latex.

Examples

1
one_combination(c(5, 0, 2, 1))

innager/Umoments documentation built on April 17, 2018, 6:20 p.m.