A Note on the Characterization of the Normal Distribution | Zendy

Ahsanullah M. | Zendy

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A Note on the Characterization of the Normal Distribution

Author(s) -

Ahsanullah M.

Publication year - 1987

Publication title -

biometrical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.108

H-Index - 63

eISSN - 1521-4036

pISSN - 0323-3847

DOI - 10.1002/bimj.4710290721

Subject(s) - independent and identically distributed random variables , mathematics , degrees of freedom (physics and chemistry) , distribution (mathematics) , f distribution , square (algebra) , normal distribution , characterization (materials science) , random variable , combinatorics , chi square test , distribution function , function (biology) , statistics , mathematical analysis , probability distribution , physics , geometry , quantum mechanics , optics , evolutionary biology , biology

Suppose X 1 , X 2 ,…, X n 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)∑ i=1 nX 2 i is a chi‐square with n degrees of freedom and (ii) nX ¯ 2 is a chi‐square with 1 degrees of freedom where X ¯=1/n ∑ i=1 nX i . Here the above two properties are utilized to characterize the normal distribution.

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