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Student’s t Increments

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Open Journal of Statistics 2016年第1期6卷 156-171页

作者： daniel T. cassidy Department of Engineering Physics McMaster University Hamilton Canada

Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t increments are independent draws from not-truncated, truncated, and effectively truncated Student’s t-distributions with shape parameters and can be used to create random walks. It is found that sample paths created from truncated and effectively truncated Student’s t-distributions are continuous. Sample paths for Student’s t-distributions are also continuous. Student’s t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.

关键词： Student’s t-Distribution Truncated Effectively Truncated Cauchy Distribution Random Walk Sample Paths Continuity

A Multivariate Student’s t-Distribution

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Open Journal of Statistics 2016年第3期6卷 443-450页

作者： daniel T. cassidy Department of Engineering Physics McMaster University Hamilton ON Canada

A multivariate Student’s t-distribution is derived by analogy to the derivation of a multivariate normal (Gaussian) probability density function. This multivariate Student’s t-distribution can have different shape parameters for the marginal probability density functions of the multivariate distribution. Expressions for the probability density function, for the variances, and for the covariances of the multivariate t-distribution with arbitrary shape parameters for the marginals are given.

关键词： Multivariate Student’s t Variance Covariance Arbitrary Shape Parameters

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

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Open Journal of Statistics 2012年第5期2卷 519-525页

作者： daniel T. cassidy Department of Engineering Physics McMaster University Hamilton Canada

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.

关键词： Asset Pricing Student’s t-Distribution Cauchy Truncation Moments Kurtosis

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我的母亲超级棒

新东方英语（中英文版） 2010年第5期 44-47页

作者： daniel cassidy 辛献云

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我的母亲多丽丝·弗朗西丝·卡西迪模样漂亮，笑声爽朗，反应敏捷。她聪明、机敏、足智多谋，而且是全天下最富有爱心的母亲。她和任何人都能聊上几句：门卫、邻居、饭店服务生、售货员、公共汽车上邻座的人，超市收银处排队的女士。她喜欢与人打交道。

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