DOI Number :
Hits : 20

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


Abstract.

Let X1, X2, ..be 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

Download Article
 
Bahasa Indonesia | English
 
 
 

Notification:

Begin on 10 October 2014 this website is no longer activated for article process in Journal of Mathematical and Fundamental Sciences, Journal of Engineering and Technological Sciences, Journal of ICT Research and Applications and Journal of Visual Art and Design. The next process will be proceeded under new website at http://journals.itb.ac.id.

For detail information please contact us to: journal@lppm.itb.ac.id.

 
       
       
       ITB Journal Visitor Number #19131602       
       Jl. Tamansari 64, Bandung 40116, Indonesia Visitor IP Address #       
       Tel : +62-22-250 1759 ext. 121 2011 Institut Teknologi Bandung       
       Fax : +62-22-250 4010, +62-22-251 1215 XHTML + CSS + RSS       
       E-mail : journal@lppm.itb.ac.id or proceedings@lppm.itb.ac.id Developed by AVE