Sampling function

In statistics , a sampling function , also called statistics , is exactly what the name says, namely a function of the sample . A sample function summarizes the information from the sample in the desired form. Examples of sample functions are estimation functions , test variables (test statistic, test variable, test function) or the limit of a confidence interval . Well-known sampling functions are sample mean , sample variance , sample median , and so on.

definition

The random variables are a sample of the scale , continues to be ${\displaystyle X_{1},\ldots ,X_{n}}$ ${\displaystyle n}$

${\displaystyle g:\mathbb {R} ^{n}\to \mathbb {R} }$

a measurable function . Then the random variable is called

${\displaystyle G=g(X_{1},\ldots ,X_{n})}$

a sampling function .

The measurability of the function guarantees that it is a random variable. ${\displaystyle g}$ ${\displaystyle G}$

literature

• Papula, Lothar ,: Mathematics for Engineers and Natural Scientists Volume 3: Vector analysis, probability calculation, mathematical statistics, error and compensation calculation . 7th edition. 2016. Springer Vieweg, Wiesbaden 2016, ISBN 978-3-658-11924-9 .