%0 Journal Article
%T Effective Truncation of a Student¡¯s <i>t</i>-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture
%A Daniel T. Cassidy
%J Open Journal of Statistics
%P 519-525
%@ 2161-7198
%D 2012
%I Scientific Research Publishing
%R 10.4236/ojs.2012.25067
%X A Student¡¯s <i>t</i>-distribution is obtained from a weighted average over the standard deviation of a normal distribution, ¦Ò, when 1/¦Ò is distributed as chi. Left truncation at q of the chi distribution in the mixing integral leads to an effectively truncated Student¡¯s <i>t</i>-distribution with tails that decay as exp (-q<sup>2</sup>t<sup>2</sup>). The effect of truncation of the chi distribution in a chi-normal mixture is investigated and expressions for the pdf, the variance, and the kurtosis of the t-like distribution that arises from the mixture of a left-truncated chi and a normal distribution are given for selected degrees of freedom <u>&lt;</u>5. This work has value in pricing financial assets, in understanding the Student¡¯s <i>t</i>--distribution, in statistical inference, and in analysis of data.
%K Asset Pricing
%K Student¡¯s &lt
%K i&gt
%K t&lt
%K /i&gt
%K -Distribution
%K Cauchy
%K Truncation
%K Moments
%K Kurtosis
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=25549