Effective Truncation of a Student’s *t*-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture

Author(s)
Daniel T. Cassidy

Abstract

A Student’s*t*-distribution is obtained from a weighted average over the standard deviation of a normal distribution, σ, when 1/σ is distributed as chi. Left truncation at q of the chi distribution in the mixing integral leads to an effectively truncated Student’s *t*-distribution with tails that decay as exp (-q^{2}t^{2}). 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 __<__5. This work has value in pricing financial assets, in understanding the Student’s *t*--distribution, in statistical inference, and in analysis of data.

A Student’s

Cite this paper

D. Cassidy, "Effective Truncation of a Student’s*t*-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture," *Open Journal of Statistics*, Vol. 2 No. 5, 2012, pp. 519-525. doi: 10.4236/ojs.2012.25067.

D. Cassidy, "Effective Truncation of a Student’s

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