In this article, I discuss the extent to which Kolmogorov drew upon von Mises’ work in addressing the problem as to why probability is applicable to events in the real world, which I refer to as the applicability problem. In particular, I highlight the role of randomness in Kolmogorov’s account, and I argue that this role differs significantly from the role that randomness plays in von Mises’ a...

A generalization of the von Mises distribution, which is broad enough to cover unimodality as well as multimodality, symmetry as well as asymmetry of circular data, has shown up in different contexts. We study this distribution in some detail here and discuss its many features, some inferential and computational aspects, and we provide some important results including characterization propertie...

We introduce the Unscented von Mises–Fisher Filter (UvMFF), a nonlinear filtering algorithm for dynamic state estimation on the n-dimensional unit hypersphere. Estimation problems on the unit hypersphere occur in computer vision, for example when using omnidirectional cameras, as well as in signal processing. As approaches in literature are limited to very simple system and measurement models, ...

Motivated by applications to goodness of fit degenerate U-statistics testing, the Jackknife empirical likelihood approach for U-statistics is generalized to degenerate U-statistics. The proposed empirical likelihood based goodness of fit tests are asymptotically distribution free. The asymptotic theory for testing shift of location, spatial depth testing for central symmetry, Cramér-von Mises t...

In this paper, we report the finite element method (FEM) simulation of double-clamped graphene nanoelectromechanical (NEM) switches. Pull-in and pull-out characteristics are analyzed for graphene NEM switches with different dimensions and these are consistent with the experimental results. This numerical model is used to study the scaling nature of the graphene NEM switches. We show the possibi...

Circular data are commonly encountered in the earth sciences and statistical descriptions and inferences about such data are necessary in structural geology. In this paper we compare two statistical distributions appropriate for complex circular data sets: the mixture of von Mises and the projected normal distribution. We show how the number of components in a mixture of von Mises distribution ...

Penalizing the model complexity is necessary to avoid overfitting when the number of data samples is low with respect to the number of model parameters. In this paper, we introduce a penalization term that places an independent prior distribution for each parameter of the multivariate von Mises distribution. We also propose a circular distance that can be used to estimate the Kullback–Leibler d...

The von Mises distribution is often useful for modelling circular data problems. We consider a model for which von Mises data is contaminated with a certain proportion of points uniformly distributed around the circle. Maximum likelihood estimation is used to produce parameter estimates for this mixture model. Computational issues involved with obtaining the maximum likelihood estimates for the...