We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving limit theorems resulting in non-Gaussian, scale-invariant diffusions. We apply the generalized characteristic functions in combination with a martingale const...

How to test the effect of density estimation methods is the key problem in the statistics. This paper presents a new criterion for assessing the effect of density estimation to select the suitable density estimation method, using the maximum-entropy non-Gaussian measurement. Comparing withχ2-test and Dn-test, the method avoids the problem of the data interval division, and it is suitable for an...

To develop 8 reliable computer vision system, the employed algorithm must guarantee good output quality. In this Study. to ensure t h 0 quality of the pose estimated from line features. two simple teet functions based on Statistical hypothesis testing are defined. First, an error function based on the relation between the line features and Some quality thresholds is defined. By using the first ...

The motivation for the work in this article is the setting in which a number of treatments are available for evaluation in phase II clinical trials and where it may be infeasible to try them concurrently because the intended population is small. This paper introduces an extension of previous work on decision-theoretic designs for a series of phase II trials. The program encompasses a series of ...

In this paper we present statistical models for text which treat words with higher frequencies of occurrence in a sensible manner, and perform better than widely used models based on the multinomial distribution on a wide range of classification tasks, with two or more classes. Our models are based on the Poisson and Negative-Binomial distributions, which keep desirable properties of simplicity...

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...

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy ε between the chaperone and the chain and the chaperone concentration N(c) can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation pro...

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...

A simple argument based on the distribution of individuals amongst discrete resource sites is used to show how the form of single species population models depends on the type of competition between, and the spatial clustering of, the individuals. For scramble competition between individuals, we confirm earlier demonstrations that the Ricker model is a direct consequence of a uniform random dis...

We use the multifractal formalism to describe the effects of dissipation on Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds number experiments and direct numerical simulation data. We show that this approach reproduces the shape evolution of velocity increment probability density functions from Gaussian to stretched exponentials as the time lag decreases from integra...