#### Sponsor

Portland State University. Dept of Mathematics

#### Date of Award

5-1-1970

#### Document Type

Thesis

#### Degree Name

Master of Science (M.S.) in Mathematics

#### Department

Mathematics

#### Physical Description

1 online resource (51, [1] leaves)

#### Subjects

Distribution (Probability theory)

#### DOI

10.15760/etd.730

#### 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.

#### Persistent Identifier

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

#### Recommended Citation

Wayland, Russell James, "Distribution of the sum of independent unity-truncated logarithmic series variables" (1970). *Dissertations and Theses.* Paper 730.

https://pdxscholar.library.pdx.edu/open_access_etds/730

10.15760/etd.730

## Description

Portland State University. Dept of Mathematics