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Investigation of The Limiting Behavior of The Sequence of Density Ratios in A Family of Non-Central t-Distribution

Sunardi Wirjosudirdjo,

Data & Software Engineering Research Group
STEI-ITB, Jl. Ganeca No.10, Bandung 40132, Indonesia


Let X1, X2, a sequence of noncentral t-distributed random variables with parameter θ. In this paper we investigate the limiting behavior of density ratios of X0. This is an example of the family of distributions discussed in [4].Here, we derive the results of David and Kurskall [2] in a slightly more general form and a stronger result is obtained, namely:

If θ1 < θ2 are two parameters and Rn12) is the density ratio of Xn, then there is  θ0 such that the limit of Rn is 0 with respect  to θ<θ0 and is ∞  with respect  to θ>θ0. With respect to θ=θ0, the limit infimum is 0 and the limit supermum is ∞. It is also shown that θ0 is between 0 and (θ12).

Keywords: mathematics, density ratio, t-distribution

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