First Advisor

Jagdish C. Ahuja

Term of Graduation

Spring 1970

Date of Publication

5-20-1970

Document Type

Thesis

Degree Name

Master of Science (M.S.) in Mathematics

Department

Mathematics

Language

English

Subjects

Distribution (Probability theory)

DOI

10.15760/etd.730

Physical Description

1 online resource (51 pages)

Abstract

Let X1, X2, ..., Xn be n independent and identically distributed random variables having the unity-truncated logarithmic series distribution with probability function given by f(x;θ) = αθX/x x ε T where α = [-log(1-θ) - θ]-1, 0 < θ < 1, and T = {2,3,...,∞}. Define their sum as Z = X1 + X2 + ... + Xn.

We derive here the distribution of Z, denoted by p(z;n,θ), using the inversion formula for characteristic functions, in an explicit form in terms of a linear combination of Stirling numbers of the first kind. A recurrence relation for the probability function p(z;n,θ) is obtained and is utilized to provide a short table of p(z;n,θ) for certain values of n and θ. Furthermore, some properties of p(z;n,θ) are investigated following Patil and Wani [Sankhya, Series A, 27, (1965), 271-280].

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Comments

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Persistent Identifier

https://archives.pdx.edu/ds/psu/9559

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