Parameter Estimation for Truncated Exponential Families

Summary

The multiparameter exponential families of probability density functions include many commonly used densities such as the normal, gamma, and beta, and many others besides. We consider the general parameter estimation problem for these families, given observations that are restricted (i.e. truncated) to the closed interval [a,b]. We show how to find maximum likelihood estimators using Newton-Raphson iteration, but observe that in general this technique requires numerical integration within each iteration. Then we give a new non-iterative method for obtaining the desired estimators for the parameter vector. An example using the generalized Inverse Gaussian is given.