Date of Award

12-2006

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Advisor

Gallagher, Colin M

Abstract

A new method is required for change-point testing of precipitation data that is capable of applying valid precipitation models. First, stochastic precipation models are researched and classified. Typically, the occurrence of rain is modeled using a two-state, first-order Markov chain, and the intensity of rain is modeled using a two-parameter gamma distribution. Using the likelihood ratio test statistic, methods are devoloped for testing for fixed and unknown change-points. These methods are developed for various models, including the MC/gamma model and simplified versions. The distribution of the LRT is unknown, however its asymptotic distribution is known for both the fixed and unknown change-point tests. First, the asymptotic converegence rates are analyzed using simulation, and then the power of the test is also analyzed using simulation. Finally the test is applied to real data, and the results are analyzed.

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