8.7. Suppose Y y1; ... ; yn T are independent gamma random variables with unknown...

8.7. Suppose Y ¼ ð y1; ... ; ynÞ T are independent gamma random variables with unknown index k and mean mi ¼ gð P j bjxijÞ, where g is a known function, b ¼ ðb1; ... ; bJ Þ are unknown regression coefficients, and xi1; ... ; xiJ are the values of covariates X1; ... ; XJ for case i. For what choice of g does Y belong to the regular J þ 1 parameter exponential family, and what are the natural parameters and complete-data sufficient statistics?