## The Annals of Mathematical Statistics

### On the Characteristic Functions of the Distributions of Estimates of Various Deviations in Samples from a Normal Population

M. Kac

#### Abstract

An explicit formula for the characteristic function of the deviation $\frac{1}{n} \sum_n {k=1}\|X_k - \bar X\|^\alpha,\quad\alpha > 0,$ is derived for samples from a normal population. For $\alpha = 1$ one can calculate the probability density function but the result does not seem to be in complete agreement with a recent formula of Goodwin [1].

#### Article information

Source
Ann. Math. Statist., Volume 19, Number 2 (1948), 257-261.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177730250

Digital Object Identifier
doi:10.1214/aoms/1177730250

Mathematical Reviews number (MathSciNet)
MR25120

Zentralblatt MATH identifier
0041.46108

JSTOR