The Goulden–Jackson cluster method is a powerful tool for counting words by occurrences of prescribed subwords, and was adapted Elizalde Noy permutations consecutive patterns. In this paper, we lift the to Malvenuto–Reutenauer algebra. Upon applying standard homomorphisms, our result specializes both as well q-analogue which keeps track inversion number statistic. We construct additional homomo...

Using the nonlinear coherent states method, a formalism for the construction of the coherent states associated to ”inverse bosonic operators” and their dual family has been proposed. Generalizing the approach, the ”inverse of f -deformed ladder operators” corresponding to the nonlinear coherent states in the context of quantum optics and the associated coherent states have been introduced. Fina...

The inverse Weibull distribution can be readily applied to a wide range of situations including applications in medicine, reliability and ecology. In this article we introduce a new model of generalized inverse Weibull distribution referred to as the Exponentiated generalized inverse distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment gener...

The statistics major index and inversion number, usually defined on ordinary words, have their counterparts in signed words, namely the socalled flag-major index and flag-inversion number. We give the construction of a new transformation on those signed words that maps the former statistic onto the latter one. It is proved that the transformation also preserves two other set-statistics: the inv...

In this work we analyzed the blinking statistics data of single CdSe/ZnS quantum dots at very short times to test some predictions of the diffusion-controlled electron transfer (DCET) model. Using autocorrelation function (ACF) approach we could extract the exponent of the inverse power-law blinking statistics down to 1 micros. Such an approach also minimizes human subjectivity in choosing a bi...

This article examines the consistency, interpretation and application of Bayes factors constructed from standard test statistics. Primary conclusions are that Bayes factors based on multinomial and normal test statistics are consistent for suitable choices of the hyperparameters used to specify alternative hypotheses, and that such constructions can be extended to obtain consistent Bayes factor...

The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices [1, 2]. Such a distribution typically goes through a maximum at a time coined the optimal investment horizon, τ ρ , which defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels o...