Effective Truncation of a Student’s <i>t</i>-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture

• 作者: Daniel T. Cassidy
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: Asset Pricing Student’s T-DISTRIBUTION Cauchy TRUNCATION Moments Kurtosis
• 年，卷（期）: 2012,（5）
• 页码范围: 519-525
• 页数: 7页
• 分类号: O1

摘要

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 (-q2t2). 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.