Differential Relations, in the Original Parameters, which Determine the First Two Moments of the Multiparameter Exponential Family
Richard A. Johnson, Joseph N. Ladalla, S. T. Liu · The Annals of Statistics · 1979
We study general multiparameter exponential families of distribution and obtain differential equations relating the first two moments of the sufficient statistics to the normalization constant. Another result illuminates the structure of both the second order partial derivatives of the likelihood and their expected values.