Consider the Gamma distribution:

(a) Write the likelihood and the the log-likelihood functions.

(b) Find the score vector and Hessian matrix.

(c) Write down the Newton-Raphson iterative steps to find the maximum likelihood estimators.

Consider the Gamma distribution of the form given by f(x; a, B) = Ba T(a) ra-1 exp(-Bx), 0 0. (a) Write the likelihood and the the log-likelihood functions. (b) Find the score vector S(a, B), and Hessian H(a, B) matrix. (c) Write down the Newton-Raphson iterative steps to find the maximum likelihood estimators for a and B