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Title: A Class of Symmetric Distributions with Bell-shaped Densities on Finite Intervals
Authors: Abrar Bader AL-Mukhaizeem 
Supervisor: Prof. Ahmad Reza Soltani
Degree Awarded: Master Degree in: Statistics and Operation Research
Keywords: Distribution with bell-shaped density on finite intervals; Two sided powerdistribution;Dirichletrandomvectors;Symmetricdistributionon(0,1);characterizations of random variable; Simulations
Issue Date: 2019
Publisher:  Kuwait university - college of graduate studies
Abstract: In this thesis, we introduce and study certain symmetric classes of continuous random variables with bell shaped density functions defined on finite intervals. Specifically, we study the random variables, defined over the interval (0,1), that are of the form X = W +ΘV, where the random vector (W,V) follows a Dirichlet distribution of order k = 3, with parameters (α,β,α), and Θ is a continuous random variable with a symmetric distribution defined over (0,1). We investigate the properties of the joint probability distribution function of X, Θ and the marginal distribution function of X. We investigate how different probability distributions for Θ affect the distribution of X. Specifically, we exam the case when Θ follows a Beta(γ,γ) distribution and the case when Θ follows a triangular distribution. For both distributions, we determine the marginal distribution of X analytically, and investigate estimation procedures for the distribution parameters using both simulated and real data.
Appears in Programs:0480 Statistics & Operations Research

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