This method calculates semi-invariants from polynomial transformations of random variables, suggesting new techniques for statistical analysis.
Let η = Q(ξ ) be the polynomial transformation of the random variable ξ. The following rule is introduced in this article in order to calculate the semi-invariants of η from the semi-invariants of ξ. It is necessary 1. to express the moments of η in terms of those of ξ according to (III), 2. to replace in (III) the expression for the moments of ξwith their semi-invariants according to (I.a), 3. to cancel some terms in the expression obtained according to the law formulated in the theorem. By employing this rule in § 4, we have calculated all the semi-invariants of the random function depending quadratically on Laplace’s function.
No takes yet. Share an insight, caveat, or question.
Leonov et al. (1959) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: