Date of Publication

5-1-1970

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, [1] leaves)

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;0) = ᵅθX ⁄ x x ε T where α = [ -log(1-θ) -θ ] 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 pCz;n,8) for certain values of n and θ. Furthermore, some properties of p(z;n,θ) are investigated following Patil and Wani [Sankhla, Series A, 27, (1965), 27l-280J.

Rights

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

Comments

Portland State University. Dept of Mathematics

Persistent Identifier

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

Share

COinS