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The natural exponential families (NEF) play an important role in many fields of statistics. Two subclasses of NEF have interesting mathematical properties and have therefore been investigated by many researchers. These two subfamilies contain the distributions with quadratic variance function (NEF-QVF) and with cubic variance function (NEF-CVF), respectively.

Bhattacharrya and Kshirsagar Lower Bounds for the Natural Exponential Family (NEF)