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.
| Identifer | oai:union.ndltd.org:pdx.edu/oai:pdxscholar.library.pdx.edu:open_access_etds-1729 |
| Date | 01 May 1970 |
| Creators | Wayland, Russell James |
| Publisher | PDXScholar |
| Source Sets | Portland State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Dissertations and Theses |
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