Ng, Ka Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 45-47). / Abstracts in English and Chinese. / Introduction --- p.v / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- Noncommutative probability spaces and Free in- dependence --- p.1 / Chapter 1.2 --- C*-probability spaces --- p.4 / Chapter 1.3 --- Fock spaces --- p.5 / Chapter 1.4 --- Cauchy transform and R-transform of probability measures with bounded support --- p.7 / Chapter 1.5 --- Helton-Howe formula --- p.8 / Chapter 1.6 --- Stieltjes inversion formula --- p.9 / Chapter 1.7 --- Pick functions --- p.11 / Chapter 2 --- Free convolution and R-transform --- p.13 / Chapter 2.1 --- Additive free convolution and R-transform --- p.13 / Chapter 2.2 --- R-transform and algebraic Cauchy transform --- p.18 / Chapter 2.3 --- Properties of R-transform --- p.26 / Chapter 2.4 --- Properties of --- p.29 / Chapter 3 --- Examples of free convolution --- p.32 / Chapter 3.1 --- Measures with compact support --- p.32 / Chapter 3.2 --- Examples of free convolution --- p.33 / Chapter 4 --- Free Central Limit Theorem --- p.42 / Bibliography --- p.45

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.

1v. (various paging) : / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (D.Sc.)--University of Adelaide, Dept. of Mathematical Sciences, 1981

Thesis (Ph. D.)--Oregon State University, 1969. / Typescript. Includes bibliographical references (leaf 43). Also available on the World Wide Web.

Includes bibliographical references

Thesis (M.S.)--Oregon Graduate Center, 1977.

Thesis--University of Florida. / Description based on print version record. Manuscript copy. Vita. Bibliography: leaves 117-119.

Thesis--University of Illinois, 1962. / Vita. Includes bibliographical references (leaf 49).

Thesis--M. Phil., University of Hong Kong, 1987.

Thesis (Ph. D.)--University of Hong Kong, 1984.