Consider a population of m-type individuals labelled by {1,2,...,m}. Let x=(x_1,x_2,...,x_m) denote the relative frequencies of all types with x_i denoting the relative frequency of type i for 1<i<m. For a random sample of size 2 from the population, the probability that the individuals of the sample are of the same type is given by H= sum of the squares of x_i's up to m. In this thesis, we focus on the case where x = (x_1,x_2,...x_m) is a random vector. The quantity H appears in various fields of study. For instance, it is associated with the Shannon entropy in communication, the Herfindahl-Hirschman index in economics and known as the homozygosity in population genetics. In Feng (2010), fluctuation theorems for the infinite dimensional case of H are considered. In this thesis we present, under a moment assumption, a Central Limit Theorem (CLT) associated with H and present as examples the Gamma subordinator case, which is a well known result by Griffiths (1979), and the generalized Gamma subordinator case. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/25133 |
| Date | January 2019 |
| Creators | Agbewu, Bright Mawusi Komla |
| Contributors | Feng, Shui, Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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