On a characterization of the normal distribution by means of identically distributed linear forms
β Scribed by M Riedel
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 476 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0047-259X
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π SIMILAR VOLUMES
In this paper a series representation of the joint density and the joint distribution of a quadratic form and a linear form in normal variables is developed. The expansion makes use of Laguerre polynomials. As an example the calculation of the joint distribution of the mean and the sample variance i
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 freed