๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A Note on the Characterization of the Normal Distribution

โœ Scribed by Dr. M. Ahsanullah

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
127 KB
Volume
29
Category
Article
ISSN
0323-3847

No coin nor oath required. For personal study only.

โœฆ Synopsis

Suppose X,, X,, ..., X, are independent and identically distributed random variables with absolutely continuous distribution function F. It is known that if F is standard normal distribution then (i) 2 X : is a chi-square with n degrees of freedom and (ii) nX2 is a chi-square with 1 degrees of freedom where i=-2 Xi. Here the above two propertiea are utilized to characterize the normal distribution. n

๐Ÿ“œ SIMILAR VOLUMES

A Characterization of the Bivariate Expo
A Characterization of the Bivariate Exponential Distribution
โœ N. U. Nair; V. K. R. Nair ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 231 KB

In this article a characterisation of the Gumbel's Bivariate Exponential Distribution is established on the basis of the propertiea of the conditional expectation of the component variables. The characterieing property is propoeed as the definition of lack of memory in the biveriate case.