**Inversion Theorem:**

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

φ (t) being the characteristic function of the distribution.

**Corollary**:

If φ (t) is absolutely integrable over R' i.e. if

**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 & f

_{1}(.) and f

_{2}(.) to be identical is that their characteristics functions

φ

_{1}(t) and φ

_{2}(t) are identical.

## No comments:

Write comments