Title page for etd-0624108-184139

URN etd-0624108-184139 Nan-cheng Su sunanchen@gmail.com This thesis had been viewed 5355 times. Download 1882 times. Applied Mathematics 2007 2 Ph.D. English An Investigation of Distribution Functions 2008-06-07 74 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 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. Mong-Na Lo Huang - chair Fu-Chuen Chang - co-chair Jyh-Cherng Su - co-chair Mei-Hui Guo - co-chair Ray-Bing Chen - co-chair Wen-Jang Huang - advisor indicate in-campus access immediately and off_campus access in a year 2008-06-24

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