A metric approach to investigation of the stability of Pólya theorem on characterization of the normal distribution
✍ Scribed by I. S. Shiganov
- Publisher
- Springer US
- Year
- 1986
- Tongue
- English
- Weight
- 647 KB
- Volume
- 34
- Category
- Article
- ISSN
- 1573-8795
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📜 SIMILAR VOLUMES
If X1 and X2 are independent and identically distributed (i.i.d.) random variables with ÿnite variance, then (X1 + X2)= √ 2 has the same distribution as X1 if and only if X1 is normal with mean zero (Polya, 1923, Math. Zeitschrift 18, 96 -108). About ten authors devoted their works to stability prob
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