one_combination: Generate symbolic expression for expectation
In Umoments: Unbiased Central Moment Estimates

Description Usage Arguments Details Value Examples

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

1	one_combination(powvect, smpsize = "n")

`powvect`	vector of non-negative integers representing exponents j[1], ..., j[m] of non-central moments in expectation (see "Details"). The position (index) of an element of this vector indicates a corresponding moment, e.g. for E(\overline{X}^5 \overline{X^4}), `powvect = c(5, 0, 0, 1)`. Thus the vector will have `m` elements if `m`'th is the highest moment.
`smpsize`	symbol to be used for sample size. Defaults to `"n"`.

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.

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.