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}), |
smpsize |
symbol to be used for sample size. Defaults to |
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.
1 | one_combination(c(5, 0, 2, 1))
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