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You searched for subject:(generalized Dirichlet model). Showing records 1 – 2 of 2 total matches.

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Texas A&M University

1. Shirazi, Mohammadali. Advanced Statistical Methods for Analyzing Crash Datasets with Many Zero Observations and a Long Tail: Semiparametric Negative Binomial Dirichlet Process Mixture and Model Selection Heuristics.

Degree: PhD, Civil Engineering, 2018, Texas A&M University

In this dissertation, first, a flexible model is introduced using a mixture of the Negative Binomial (NB) distribution and a random distribution characterized by Dirichlet process (DP) (referred to as NB-DP). This modeling approach aims to provide a greater flexibility to the NB distribution in order to overcome different limitations of the NB distribution, such as modeling data with many zero observations and a long (or heavy) tail. Application of the NB-DP to two observed datasets indicated that the NB-DP model offers a better performance than the NB when data are characterized by many zero observations and a long tail. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data or domain. Second, a methodology is proposed to select the most-likely-true sampling distribution between potential alternatives, based on the characteristic of the data, before fitting the models. The proposed methodology employs two analytic tools: (1) Monte Carlo Simulations and (2) Machine Learning Classifiers, to design simple heuristics to predict the label of the most-likely-true distribution for analyzing data. Next, this method was first applied to investigate when the Poisson-lognormal is preferred over the NB. The results showed that the kurtosis, skewness and percentage of zeros are the main summary statistics needed to select a distribution between these two alternatives. Then, it was investigated when the Negative Binomial Lindley (NB-L) is preferred over the NB. The results showed that the skewness, coefficient of variation, kurtosis, variance-to-mean ratio, and the percentage of zeros are among the most important summary statistics (or predictors) required to select a logical distribution between the NB and NB-L. Advisors/Committee Members: Lord, Dominique (advisor), Hart, Jeffrey (committee member), Quadrifoglio, Luca (committee member), Zhang, Yunlong (committee member).

Subjects/Keywords: Dirichlet process; Model Selection; Negative Binomial; Generalized Linear Model; Crash Data

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

APA (6th Edition):

Shirazi, M. (2018). Advanced Statistical Methods for Analyzing Crash Datasets with Many Zero Observations and a Long Tail: Semiparametric Negative Binomial Dirichlet Process Mixture and Model Selection Heuristics. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/174406

Chicago Manual of Style (16th Edition):

Shirazi, Mohammadali. “Advanced Statistical Methods for Analyzing Crash Datasets with Many Zero Observations and a Long Tail: Semiparametric Negative Binomial Dirichlet Process Mixture and Model Selection Heuristics.” 2018. Doctoral Dissertation, Texas A&M University. Accessed May 09, 2021. http://hdl.handle.net/1969.1/174406.

MLA Handbook (7th Edition):

Shirazi, Mohammadali. “Advanced Statistical Methods for Analyzing Crash Datasets with Many Zero Observations and a Long Tail: Semiparametric Negative Binomial Dirichlet Process Mixture and Model Selection Heuristics.” 2018. Web. 09 May 2021.

Vancouver:

Shirazi M. Advanced Statistical Methods for Analyzing Crash Datasets with Many Zero Observations and a Long Tail: Semiparametric Negative Binomial Dirichlet Process Mixture and Model Selection Heuristics. [Internet] [Doctoral dissertation]. Texas A&M University; 2018. [cited 2021 May 09]. Available from: http://hdl.handle.net/1969.1/174406.

Council of Science Editors:

Shirazi M. Advanced Statistical Methods for Analyzing Crash Datasets with Many Zero Observations and a Long Tail: Semiparametric Negative Binomial Dirichlet Process Mixture and Model Selection Heuristics. [Doctoral Dissertation]. Texas A&M University; 2018. Available from: http://hdl.handle.net/1969.1/174406


Mahatma Gandhi University

2. Thomas, Seemon. Some extensions of dirichlet models and their applications; -.

Degree: Statistics, 2007, Mahatma Gandhi University

The thesis starts with a few words on Dirichlet himself. The properties of standard real type-1 and type-2 Dirichlet distributions are then discussed. Matrix-variate analogues of type-1 and type-2 Dirichlet models are also presented. A survey of some of the important areas of applications and extensions of Dirichlet models is attempted. All these are done in the first chapter. In the second chapter we introduce a new extension of type-1 Dirichlet model both in scalar variables case and in the matrix-variate case. The generalization of type-1 Dirichlet model in the scalar variables case is derived by using a property which we will call as a short memory property . Several properties of this new model, which are applicable in many fields, are presented. Here the matrix-variate analogue of an extension of a type-1 Dirichlet model is developed and its properties are also discussed. In certain studies, successive sums of variables also enter into the picture. Hence an extension of the type-2 Dirichlet model with successive sums incorporated into it, is introduced in the third chapter. Many types of properties of this new model are studied which enhance the possibility of application in different directions. Further, the matrixvariate analogue of this new model is given and its properties are also examined. The fourth chapter explores the application of a generalized real type-1 Dirichlet model in multivariate statistical analysis. It is shown that the exact null distribution of likelihood ratio criteria for testing a number of hypotheses on the parameters of one or more multivariate Gaussian populations can be obtained as a marginal distribution of this generalized Dirichlet model having a specific set of parameters. The exact distribution of the likelihood ratio criterion so obtained has a very simple and general format for every p. Various types of properties and relations involving hypergeometric series are also established.

References given chapters wise

Advisors/Committee Members: Thannippara, Alex.

Subjects/Keywords: geometrical probability; generalized Dirichlet model; beta density; short memory property; neutrality principle; matrix-variate distribution; Jacobians of matrix transformations; Meijer s G-function; likelihood ratio criterion; exact distribution

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

APA (6th Edition):

Thomas, S. (2007). Some extensions of dirichlet models and their applications; -. (Thesis). Mahatma Gandhi University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/7129

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Thomas, Seemon. “Some extensions of dirichlet models and their applications; -.” 2007. Thesis, Mahatma Gandhi University. Accessed May 09, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/7129.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Thomas, Seemon. “Some extensions of dirichlet models and their applications; -.” 2007. Web. 09 May 2021.

Vancouver:

Thomas S. Some extensions of dirichlet models and their applications; -. [Internet] [Thesis]. Mahatma Gandhi University; 2007. [cited 2021 May 09]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/7129.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Thomas S. Some extensions of dirichlet models and their applications; -. [Thesis]. Mahatma Gandhi University; 2007. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/7129

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.