Exponential Family of Distributions

M. Ataharul Islam () and Soma Chowdhury Biswas ()
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M. Ataharul Islam: University of Dhaka, ISRT
Soma Chowdhury Biswas: University of Chittagong, Department of Statistics

Chapter Chapter 2 in Generalized Linear Models and Extensions, 2025, pp 23-38 from Springer

Abstract: Abstract Exponential family of distributions is introduced in this chapter. It starts with two different representations of exponential family of distributions and identifies the important discrete and continuous distributions that belong to the exponential family. The rules for obtaining the expected value and variance are shown. The role of sufficiencySufficiency in employing an exponential family of distributions is discussed elaborately to provide learners and users a clear understanding about the importance of exponential family in modeling data of various types. The exponential family of distributions makes it convenient to obtain sufficient statisticsSufficient statistics and the estimation of parameters of a generalized linear model become much more appealing. The properties can be generalized for a wide spectrum for being applied to real-life data. The canonical link functionsLink function are defined and the properties are discussed. The one and multi parameter sufficiency are demonstrated with their links with exponential family of distributions for different data types and properties are highlighted.

Date: 2025
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DOI: 10.1007/978-981-96-4726-2_2

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