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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.||URI:||http://hdl.handle.net/123456789/988|
|Appears in Programs:||0480 Statistics & Operations Research|
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