Limiting distributions of two random sequences

Robert Chen, Richard Goodman and Alan Zame

Journal of Multivariate Analysis, 1984, vol. 14, issue 2, 221-230

Abstract: For fixed p (0 = 2, with probability p let {Ln, Rn} = {Ln - 1, Xn} or = {Xn, Rn - 1} according as , with probability 1 - p let {Ln, Rn} = {Xn, Rn - 1} or = {Ln - 1, Xn} according as , and let Xn + 1 be a uniform random variable over {Ln, Rn}. By this iterated procedure, a random sequence {Xn}n >= 1 is constructed, and it is easy to see that Xn converges to a random variable Yp (say) almost surely as n --> [infinity]. Then what is the distribution of Yp? It is shown that the Beta, (2, 2) distribution is the distribution of Y1; that is, the probability density function of Y1 is g(y) = 6y(1 - y) I0,1(y). It is also shown that the distribution of Y0 is not a known distribution but has some interesting properties (convexity and differentiability).

Keywords: Beta; distribution; uniform; random; variable; convexity; differentiability; moment; generating; function; confluent; hypergeometric; function; characteristic; function (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (3)

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