Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a num...

We propose an approach to the problem of the first-passage time. Our method is applicable not only to the Wiener process but also to the non-Gaussian Lévy flights or to more complicated stochastic processes whose distributions are stable. To show the usefulness of the method, we particularly focus on the first-passage time problems in the truncated Lévy flights (the so-called KoBoL processes fr...

A probability distribution can be characterized through various methods. In this paper, we have established some new characterizations of folded Student’s t distribution by truncated first moment, order statistics and upper record values. It is hoped that the results will be quite useful in the fields of probability, statistics, and other applied sciences.

Abstract The multivariate normal and the multivariate t distributions belong to the most widely used multivariate distributions in statistics, quantitative risk management, and insurance. In contrast to the multivariate normal distribution, the parameterization of the multivariate t distribution does not correspond to its moments. This, paired with a non-standard implementation in the R package...

In statistic tests, the probability distribution of the statistics is important. When samples are drawn from population N (µ, σ(2)) with a sample size of n, the distribution of the sample mean X̄ should be a normal distribution N (µ, σ(2)/n). Under the null hypothesis µ = µ0, the distribution of statistics [Formula: see text] should be standardized as a normal distribution. When the variance of ...

Closed-form approximations for the density and cumulative distribution function of the doubly noncentral t distribution are developed based on saddlepoint methods. They exhibit remarkable accuracy throughout the entire support of the distribution and are vastly superior to existing approximations. An application in finance is considered which capitalizes on the enormous increase in computationa...

Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial with frequentist solutions being unavaila...

We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate t distribution, symmetric stable laws, exponential power and Kotz distributions. In each case, the shape parameter is allowed to vary in the mixture, in addition to the location vector and the ...

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 ...