This technical report summarizes a number of results for the multivariate t distribution which can exhibit heavier tails than the Gaussian distribution. It is shown how t random variables can be generated, the probability density function (pdf) is derived, and marginal and conditional densities of partitioned t random vectors are presented. Moreover, a brief comparison with the multivariate Gau...

This Appendix is part of the article cocor: A Comprehensive Solution for the Statistical Comparison of Correlations by Birk Diedenhofen and Jochen Musch published in PLOS ONE. In the following, the formulae of all tests implemented in the R package [1] cocor (version 1.1-0) are provided. z statistics are based on a normal distribution, whereas t statistics rely on a Student’s t-distribution wit...

We construct a copula from the multivariate skew t-distribution of Azzalini and Capitanio (2003). This copula can capture asymmetric and extreme dependence between variables, and it is one of the few that is effective when the number of dimensions is high. However, two problems arise when estimating the parameters by maximum likelihood estimation. Here, we solve these problems and provide a con...

Background: The assignment of a point-level geocode to subjects' residences is an important data assimilation component of many geographic public health studies. Often, these assignments are made by a method known as automated geocoding, which attempts to match each subject's address to an address-ranged street segment georeferenced within a streetline database and then interpolate the position...

The problem of nonseparable space-time covariance functions is essential and difficult in spatiotemporal data analysis. Considering that a fully symmetric space-time covariance function is inappropriate for many spatiotemporal processes, this article provides a way to construct a non-fully symmetric nonseparable space-time correlation function from any given marginal spatial Matérn and marginal...

Alternatives to M-estimation for robust estimation of the median lethal dose in biological assays are developed. A class of link functions based on the Student-t distribution is proposed, where degrees of freedom are estimated from the data by maximum likelihood. Other alternatives include slash and finite mixture distributions. For bioassays from a pharmaceutical company, these methods extend ...

A number of recent methods developed for automatic classification of multiunit neural activity rely on a Gaussian model of the variability of individual waveforms and the statistical methods of Gaussian mixture decomposition. Recent evidence has shown that the Gaussian model does not accurately capture the multivariate statistics of the waveform samples' distribution. We present further data de...

The validity of the normal distribution as an error model is commonly tested with a (half) normal probability plot. Real data often contain outliers. The use of t-distributions in a probability plot to model such data more realistically is described. It is shown how a suitable value of the parameter nu of the t-distribution can be determined from the data. The results suggest that even data tha...

In this paper we present a new methodology to infer the implied risk-neutral distribution function from European-style options. We introduce a skewed version of the Student-t distribution, whose main advantage is that its shape depends on only four parameters, of which two directly control for the levels of skewness and kurtosis. We can thus easily vary parameters to compare different distribut...

Extending a basic statistical model can be carried out by using a parametric family of distributions that contains the basic model as a particular case but has an extra parameter, which we denote by flexibility parameter, to control the amount of flexibility or deviation from the basic model. We propose a formal framework to construct prior distributions for the flexibility parameter that place...