Question

If $X_{1}, X_{2}, \dots, X_{n}$ be independent random variable each from Gamma($\alpha, \beta$) then the jointly sufficient statistics for vector ($\alpha, \beta$) is

• A. $(\sum_{i=1}^{n} X_{i}, \prod_{i=1}^{n} X_{i})$
• B. $(\prod_{i=1}^{n} X_{i}, \sum_{i=1}^{n} X_{i})$
• C. $(\prod_{i=1}^{n} X_{i}, \prod_{i=1}^{n} X_{i})$
• D. $(\sum_{i=1}^{n} X_{i}, \sum_{i=1}^{n} X_{i})$

Hint:

For members of the exponential family like the Gamma distribution, the sufficient statistics are simply the sums of the terms that appear in the exponent of the canonical form.

Answer 1

The Correct Option is A