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In this chapter, we review the elementary features of several basic parametric distributions for discrete random variables that form the building blocks of item response theory (IRT) and related psychometric models. Many IRT models are defined directly in terms of these distributions or their generalizations. For each distribution, we will review the form of the probability mass function (pmf), that is, the function *f*(*u*) = *PU* = *u* for a response variable *U* with that distribution, as well as some basic features of the distribution. Most of the distributions reviewed here are members of the exponential family of distributions. The textbook of DeGroot and Schervish (2001) is the primary source for the general properties of these distributions. Other useful sources include Johnson and Kotz (1969) and Novick and Jackson (1974).

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