The book acquaints researchers and graduate students with good mathematical, probabilistic and statistical knowledge, with the present-day stage of the theory of distributions derived from and/or closely connected with Lagrange expansions. The book presents a comprehensive treatment of the almost infinite number of discrete Lagrangian probability distributions that can be divided into three subsets according to their probabilistic structure: (i) basic Lagrangian distributions, (ii) delta Lagrangian distributions, and (iii) general Lagrangian distributions. Chapter 1 covers mathematical, probabilistic, and statistical results needed in the sequel. The Lagrangian distributions, modified power series distributions (a special subclass of Lagrangian distributions) and also some of their basic characteristic properties are described in Chapters 2 and 3.
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