# Randomization

Jump to: navigation, search

A statistical procedure in which a decision is randomly taken. Suppose that, given a realization $x$ of a random variable $X$ with values in a sample space $( \overline{X}\; , {\mathcal B} , {\mathsf P} _ \theta )$, $\theta \in \Theta$, one has to choose a solution $\xi$ from a measurable space $( \Xi , {\mathcal A} )$, and suppose that a family of so-called transition probability distributions $\{ Q _ {x} ( \cdot ) \}$, $x \in \overline{X}\;$, has been defined on $( \Xi , {\mathcal A} )$ such that the function $Q _ {\mathbf . } ( A)$ is ${\mathcal B}$- measurable in $x$ for every fixed event $A \in {\mathcal A}$. Then randomization is the statistical procedure of decision taking in which, given a realization $x$ of $X$, the decision is made by drawing lots subject to the probability law $Q _ {x} ( \cdot )$.

How to Cite This Entry:
Randomization. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Randomization&oldid=48430
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article