#### Sponsor

Portland State University. Dept of Mathematics

#### 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).

#### 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://doi.org/10.15760/etd.730

## Comments

Portland State University. Dept of Mathematics