Some New Probability Distributions Based on Random Extrema and Permutation Patterns

Author

Jie Hao, East Tennessee State UniversityFollow

Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

5-2014

Committee Chair or Co-Chairs

Anant P. Godbole

Committee Members

Robert M. Price Jr., Edith Seier

Abstract

In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X₁,X₂, ..., X_N, where each X_i has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where X_i is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for the continuous random variables such as Arcsine, Topp-Leone, and N is chosen to be Geometric or Zipf. Wherever appropriate, we estimate of the parameter in the one-parameter family in question and test the hypotheses about the parameter. In the last section, two permutation distributions are introduced and studied.

Document Type

Thesis - unrestricted

Recommended Citation

Hao, Jie, "Some New Probability Distributions Based on Random Extrema and Permutation Patterns" (2014). Electronic Theses and Dissertations. Paper 2344. https://dc.etsu.edu/etd/2344

Copyright

Copyright by the authors.