Friday, July 31, 2015

Inversion and Uniqueness Theorem

Inversion Theorem:
If (a-h, a+h) is the continuity interval of the distribution function, F(x), then

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φ (t) being the characteristic function of the distribution.
Corollary:
If φ (t) is absolutely integrable over R' i.e. if


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Uniqueness theorem of Characteristics Function (cf):
Characteristics functions uniquely determines the distribution i.e. a necessary & sufficient condition for two distributions with p.d.f & f1 (.) and f2 (.) to be identical is that their characteristics functions
φ 1(t) and φ 2(t) are identical. 

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