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NSYSU

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

Degree: PhD, Applied Mathematics, 2008, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0624108-184139

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

Record Details Similar Records

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

APA (6^{th} 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 (16^{th} Edition):

Su, Nan-cheng. “An Investigation of Distribution Functions.” 2008. Doctoral Dissertation, NSYSU. Accessed April 02, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0624108-184139.

MLA Handbook (7^{th} Edition):

Su, Nan-cheng. “An Investigation of Distribution Functions.” 2008. Web. 02 Apr 2020.

Vancouver:

Su N. An Investigation of Distribution Functions. [Internet] [Doctoral dissertation]. NSYSU; 2008. [cited 2020 Apr 02]. 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

2.
Akdemir, Deniz.
A Class of Multivariate *Skew* Distributions: Properties and
Inferential Issues.

Degree: PhD, Mathematics/Probability and Statistics, 2009, Bowling Green State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643

Flexible parametric distribution models that can
represent both skewed and symmetric distributions, namely skew
symmetric distributions, can be constructed by skewing symmetric
kernel densities by using weighting distributions. In this
dissertation, we study a multivariate skew family that have either
centrally symmetric or spherically symmetric kernel. Specifically,
we define multivariate skew symmetric forms of uniform, normal,
Laplace, and Logistic distributions by using the cdf's of the same
distributions as weighting distributions. Matrix variate extensions
of these distributions are also introduced herein. To bypass the
unbounded likelihood problem related to the inference about this
model, we propose an estimation procedure based on the maximum
product of spacings method. This idea also leads to bounded model
selection criteria that can be considered as alternatives to
Akaike's and other likelihood based criteria when the unbounded
likelihood may be a problem. Applications of skew symmetric
distributions to data are also considered.
*Advisors/Committee Members: McFillen, James M. (Committee Chair), Gupta, Arjun K. (Advisor).*

Subjects/Keywords: Statistics; Multivariate Skew-Symmetric Distribution; Matrix Variate Skew-Symmetric Distribution; Inference, Maximum Product of Spacings; Unbounded Likelihood, Model Selection Criterion

…account the
skewness property. *Skew* *symmetric* *distribution* is useful in many practical… …fundamental *skew* *distribution*
([5]).
2.2
*Skew*-Centrally *Symmetric* Densities… …theorem, we relate the *distribution* of the even powers of a *skew* *symmetric*
random variable to… …suitable
family of transformations. A random vector x has centrally *symmetric* *distribution* about… …line through the
origin has a *symmetric* *distribution*. The joint *distribution* of k…

Record Details Similar Records

❌

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

APA (6^{th} Edition):

Akdemir, D. (2009). A Class of Multivariate Skew Distributions: Properties and Inferential Issues. (Doctoral Dissertation). Bowling Green State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643

Chicago Manual of Style (16^{th} Edition):

Akdemir, Deniz. “A Class of Multivariate Skew Distributions: Properties and Inferential Issues.” 2009. Doctoral Dissertation, Bowling Green State University. Accessed April 02, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643.

MLA Handbook (7^{th} Edition):

Akdemir, Deniz. “A Class of Multivariate Skew Distributions: Properties and Inferential Issues.” 2009. Web. 02 Apr 2020.

Vancouver:

Akdemir D. A Class of Multivariate Skew Distributions: Properties and Inferential Issues. [Internet] [Doctoral dissertation]. Bowling Green State University; 2009. [cited 2020 Apr 02]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643.

Council of Science Editors:

Akdemir D. A Class of Multivariate Skew Distributions: Properties and Inferential Issues. [Doctoral Dissertation]. Bowling Green State University; 2009. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643

3. Chandra Girish. CONTRIBUTIONS TO STATISTICAL METHODS IN RISK ASSESSMENT AND CONTROL OF ENVIRONMENTAL POLLUTION;.

Degree: 2014, Kumaun University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/20128

newline

Subjects/Keywords: ADAPTIVE CLUSTER SAMPLING BASED ON RANKED SETS; A SYSTEMATIC APPROACH FOR UNEQUAL ALLOCATIONS FOR RANKED SET SAMPLING WITH SKEW DISTRIBUTIONS; ESTIMATION OF LOCATION AND SCALE PARAMETERS OF LOGNORMAL DISTRIBUTION USING RANKED SET SAMPLING; NEAR OPTIMAL ALLOCATION MODELS FOR SYMMETRIC DISTRIBUTIONS IN RANKED SET SAMPLING; RANKED SET SAMPLING THEORY FOR LARGE SET SIZE WITH PROBABILITY PROPORTION TO RANK SIZE MATRIX

Record Details Similar Records

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

APA (6^{th} Edition):

Girish, C. (2014). CONTRIBUTIONS TO STATISTICAL METHODS IN RISK ASSESSMENT AND CONTROL OF ENVIRONMENTAL POLLUTION;. (Thesis). Kumaun University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/20128

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Girish, Chandra. “CONTRIBUTIONS TO STATISTICAL METHODS IN RISK ASSESSMENT AND CONTROL OF ENVIRONMENTAL POLLUTION;.” 2014. Thesis, Kumaun University. Accessed April 02, 2020. http://shodhganga.inflibnet.ac.in/handle/10603/20128.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Girish, Chandra. “CONTRIBUTIONS TO STATISTICAL METHODS IN RISK ASSESSMENT AND CONTROL OF ENVIRONMENTAL POLLUTION;.” 2014. Web. 02 Apr 2020.

Vancouver:

Girish C. CONTRIBUTIONS TO STATISTICAL METHODS IN RISK ASSESSMENT AND CONTROL OF ENVIRONMENTAL POLLUTION;. [Internet] [Thesis]. Kumaun University; 2014. [cited 2020 Apr 02]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/20128.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Girish C. CONTRIBUTIONS TO STATISTICAL METHODS IN RISK ASSESSMENT AND CONTROL OF ENVIRONMENTAL POLLUTION;. [Thesis]. Kumaun University; 2014. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/20128

Not specified: Masters Thesis or Doctoral Dissertation