SEVERAL STATISTICAL RESULTS UNDER MULTINOMIAL DISTRIBUTION WITH INFINITE CATEGORIES

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Zhou, J. (2009). SEVERAL STATISTICAL RESULTS UNDER MULTINOMIAL DISTRIBUTION WITH INFINITE CATEGORIES. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

This dissertation discusses several statistical results under multinomial distribution with infinite categories. Firstly, the discussion focuses on Simpson's diversity index and Turing's formula. We established an unbiased estimate for the newly proposed Generalized Simpson's indices and the associated asymptotic properties and showed that the parameters of a multinomial distribution may be re-parameterized as a set of Generalized Simpson's diversity indices. Secondly, two-dimensional asymptotic normality of a non-parametric sample coverage estimate based on Turing's formulae was derived under a fixed underlying probability distribution {p_k; k = 1, 2, · · · } where all p_k > 0. Thirdly, the dissertation also establishes a previously unknown sufficient condition for the second order Turing's formula. The newly derived asymptotic results based on Turing's formula paves a possible way to establish a new estimating approach for Hill's tail probability model.

Details
Author

Zhou, Jun

Title

SEVERAL STATISTICAL RESULTS UNDER MULTINOMIAL DISTRIBUTION WITH INFINITE CATEGORIES

Physical Description

1 online resource (58 pages) : PDF

Date

2009

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

This dissertation discusses several statistical results under multinomial distribution with infinite categories. Firstly, the discussion focuses on Simpson's diversity index and Turing's formula. We established an unbiased estimate for the newly proposed Generalized Simpson's indices and the associated asymptotic properties and showed that the parameters of a multinomial distribution may be re-parameterized as a set of Generalized Simpson's diversity indices. Secondly, two-dimensional asymptotic normality of a non-parametric sample coverage estimate based on Turing's formulae was derived under a fixed underlying probability distribution {p_k; k = 1, 2, · · · } where all p_k > 0. Thirdly, the dissertation also establishes a previously unknown sufficient condition for the second order Turing's formula. The newly derived asymptotic results based on Turing's formula paves a possible way to establish a new estimating approach for Hill's tail probability model.

Genre

doctoral dissertations

Subjects--Topics

Statistics
Mathematics

Degree

Ph.D.

Keywords

Generalized Simpson's Biodiversity Index
Infinite Categories
Multinomial Distribution
Turing's Formula

Subject Area

Applied Mathematics

Advisor(s)

Zhang, Zhiyi

Committee Members

Dai, Ming
Sun, Yanqing
Khouja, Moutaz

Degree Note

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2009.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Zhou_uncc_0694D_10058

Permalink

http://hdl.handle.net/20.500.13093/etd:1612