The aim of this paper is to extend the notion of topological entropy for fuzzy semidynamical systems created by a self-map on a fuzzy metric space. We show that if a metric space has two uniformly equivalent metrics, then fuzzy entropy is a constant up to these two metrics. We present a method to construct chaotic fuzzy semidynamical systems with arbitrary large fuzzy entropy. We also prove tha...

There are several well-known single SNP tests presented in the literature for detecting gene-disease association signals. Having in place an efficient and robust testing process across all genetic models would allow a more comprehensive approach to analysis. Although some studies have shown that it is possible to construct such a test when the variants are common and the genetic model satisfies...

In this paper, for identifying an observable process with one of several simulation models, a uniformly most powerful invariant (UMPI) test is developed from the generalized maximum likelihood ratio (GMLR). This test can be considered as a result of a new approach to solving the Behrens-Fisher problem when covariance matrices of multivariate normal populations (compared with respect to their me...

We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local onesided composite. We describe the choice of the thresholds and the power functions of the Score Function test, of the General Likelihood Ratio test, of the Wald test and of two Bayes tests in the situation when the intensity function of the observed inhomogeneous Pois...

A test of reciprocity is often performed by analysts of social network data. This test corresponds to testing whether a parameter in an exponential family model for the adjacency matrix is zero. The uniformly most powerful unbiased test compares the observed number of mutual relations in the social network to its exact conditional distribution. As this distribution is typically only known to a ...

We take the perspective of a researcher planning a randomized trial of a new treatment, where it is suspected that certain subpopulations may benefit more than others. These subpopulations could be defined by a risk factor or biomarker measured at baseline. We focus on situations where the overall population is partitioned into two, predefined subpopulations. When the true average treatment eff...