THE LIMITS OF CERTAIN PROBABILITY DISTRIBUTIONS ASSOCIATED WITH THE WRIGHT-FISHER MODEL

Abstract

<p>In this thesis, I endeavor to solve the remaining problem in Dr.Feng's paper[8], where Dr.Feng obtain the Large Deviation Principle of the following distribution</p> <p>[equation removed]</p> <p>p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times} p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times} span.s1 {font: 13.5px Times} span.s2 {font: 15.0px Helvetica} span.s3 {font: 8.5px Helvetica} span.s4 {font: 12.0px Times} span.s5 {font: 11.5px Helvetica} span.s6 {font: 11.0px Times} span.s7 {font: 10.5px Helvetica} span.s8 {font: 6.5px Times}</p> <p>Generally speaking, the Large Deviation Principle can yield the limit distribution if its rate function has only one zero point. Unfortunately, however, the rate function in [8] involves another parameter λ. When θ(a) = -log α, λ = -k(k + l), k ≥ 1, the rate function has exactly two zero points, thus by way of the Large Deviation Principle, we can hardly know its limit distribution. Therefore, I try to figure out another way to find it. Since PD(α)(dx) is the limit of the ordered Dirichlet distribution [equation removed] as K<strong> → </strong>+∞, then IIαλ(dx) is the limit of [equation removed] I only find the limit of [equation removed] which is the case when K = 2, θ(α) = -log α, λ < 0. The result is quite unexpected!</p> <p><br /></p>