Subroutines for computing minimum variance unbiased estimators of functions of the parameters in the normal and gamma distributions

In this paper subroutines are given which calculate the uniformly minimum variance unbiased estimators (UMVUE’ s) of a broad class of functions of the parameters of the normal and gamma distributions. These subroutines employ the new expressions for the UMVUE’ s given recently by Gray, Watkins, and Schucany (1973), Woodward and Gray (1975), and Gray, Schucany, and Woodward (1976). In order to employ the subroutines here the user need only be able to provide a FORTRAN function subprogram to calculate derivatives of the function, either analytically or numerically.