相关论文: Maximum Likelihood Estimation for q-Exponential (T…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…
This paper gives a new approach for the maximum likelihood estimation of the joint of the location and scale of the Cauchy distribution. We regard the joint as a single complex parameter and derive a new form of the likelihood equation of a…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
The maximum entropy principle in Tsallis statistics is reformulated in the mathematical framework of the q-product, which results in the unique non self-referential q-canonical distribution. As one of the applications of the present…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…
We provide a semi-parametric analysis for the proportional likelihood ratio model, proposed by Luo & Tsai (2012). We study the tangent spaces for both the parameter of interest and the nuisance parameter, and obtain an explicit expression…
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
In this paper, we introduce a new class of bivariate distributions called the bivariate exponentiated extended Weibull distributions. The model introduced here is of Marshall-Olkin type. This new class of bivariate distributions contains…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized…
Tsallis' non-extensive entropy $S_q$ enables us to treat both a power and exponential evolutions of underlying microscopic dynamics on equal footing by adjusting the variable entropic index $q$ to proper one $q^*$. We propose an alternative…
Recent advances in extreme value theory have established $\ell$-Pareto processes as the natural limits for extreme events defined in terms of exceedances of a risk functional. Here we provide methods for the practical modelling of data…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
Tsallis and R\'{e}nyi entropies, which are monotone transformations of each other, are deformations of the celebrated Shannon entropy. Maximization of these deformed entropies, under suitable constraints, leads to the $q$-exponential family…
We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved…
Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…