dc.contributor.author | Lesaris, Symon M | |
dc.date.accessioned | 2019-01-29T10:05:03Z | |
dc.date.available | 2019-01-29T10:05:03Z | |
dc.date.issued | 2018 | |
dc.identifier.uri | http://hdl.handle.net/11295/105839 | |
dc.description.abstract | The goal of this project, is to demonstrate the use of special functions; in this case - hypergeometric
function in statistics. We start by deriving the basic di erence di erential
equations for birth and death processes at equilibrium and solving it iteratively using
di erent values of ln and mn. The solution of the basic di erence - di erential equations
are applied and hence obtain distributions to the: (i) Growth models; (ii) Waiting time
problems and (iii) Queuing processes as special cases of Birth and Death processes at
equilibrium.
The basic di erence di erential equations are also expressed as ratio of polynomials and
the equations are solved to obtain probability distributions in terms probability generating
function technique and hypergeometric functions.
Birth and death processes at equilibrium and their extensions based on recursive models
of Pn+1 as a function of Pn and Pn1; Katz, Crow-Bardwell, Panjer’s and Kemp’s families of
recursive models as a ratio of polynomials Pn+1
Pn
= Q(n)
R(n) ; Kapur’s recursive model as a ratio
of polynomials Pi
Pi1
.
Note that, Kapur (1978a) generalized birth and death processes are expressed in terms of
generalized hypergeometric functions at equilibrium as ratio of polynomials given;
Pi
Pi1
=
li1
mi
; mi 6= 0
where various cases of li and mi are solved.
A con uent hypergeometric series distribution is constructed using Kummer’s series is
used as a tool to construct hypergeometric function from a ratio of polynomials. Some
special cases and properties of the distributions arising from these processes are discussed. | en_US |
dc.language.iso | en | en_US |
dc.publisher | University of Nairobi | en_US |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/us/ | * |
dc.subject | Distributions Arising From Birth and Death Processes at Equilibrium and Their Extensions | en_US |
dc.title | Distributions Arising From Birth and Death Processes at Equilibrium and Their Extensions | en_US |
dc.type | Thesis | en_US |