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NSYSU

1. Su, Nan-cheng. An Investigation of Distribution Functions.

Degree: PhD, Applied Mathematics, 2008, NSYSU

The study of properties of probability distributions has always been a persistent theme of statistics and of applied probability. This thesis deals with an investigation of distribution functions under the following two topics: (i) characterization of distributions based on record values and order statistics, (ii) properties of the skew-t distribution. Within the extensive characterization literature there are several results involving properties of record values and order statistics. Although there have been many well known results already developed, it is still of great interest to find new characterization of distributions based on record values and order statistics. In the first part, we provide the conditional distribution of any record value given the maximum order statistics and study characterizations of distributions based on record values and the maximum order statistics. We also give some characterizations of the mean value function within the class of order statistics point processes, by using certain relations between the conditional moments of the jump times or current lives. These results can be applied to characterize the uniform distribution using the sequence of order statistics, and the exponential distribution using the sequence of record values, respectively. Azzalini (1985, 1986) introduced the skew-normal distribution which includes the normal distribution and has some properties like the normal and yet is skew. This class of distributions is useful in studying robustness and for modeling skewness. Since then, skew-symmetric distributions have been proposed by many authors. In the second part, the so-called generalized skew-t distribution is defined and studied. Examples of distributions in this class, generated by the ratio of two independent skew-symmetric distributions, are given. We also investigate properties of the skew-symmetric distribution. Advisors/Committee Members: Jyh-Cherng Su (chair), Wen-Jang Huang (committee member), Mei-Hui Guo (chair), Ray-Bing Chen (chair), Fu-Chuen Chang (chair), Mong-Na Lo Huang (chair).

Subjects/Keywords: skew-normal distribution; nonhomogeneous Poisson process; conditional expectation; skew-Cauchy distribution; skew-t distribution.; skew-symmetric distribution; order statistics; characterization; conditional distribution; record values; order statistics property

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Su, N. (2008). An Investigation of Distribution Functions. (Doctoral Dissertation). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0624108-184139

Chicago Manual of Style (16th Edition):

Su, Nan-cheng. “An Investigation of Distribution Functions.” 2008. Doctoral Dissertation, NSYSU. Accessed December 08, 2019. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0624108-184139.

MLA Handbook (7th Edition):

Su, Nan-cheng. “An Investigation of Distribution Functions.” 2008. Web. 08 Dec 2019.

Vancouver:

Su N. An Investigation of Distribution Functions. [Internet] [Doctoral dissertation]. NSYSU; 2008. [cited 2019 Dec 08]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0624108-184139.

Council of Science Editors:

Su N. An Investigation of Distribution Functions. [Doctoral Dissertation]. NSYSU; 2008. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0624108-184139

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