Minimally informative distributions with given rank correlation for use in uncertainty analysis

Minimum information bivariate distributions with uniform marginals and a specified rank correlation are studied in this paper. These distributions play an important role in a particular way of modeling dependent random variables which has been used in the computer code UNICORN for carrying out uncertainty analyses. It is shown that these minimum information distributions have a particular form which makes simulation of conditional distributions very simple. Approximations to the continuous distributions are discussed and explicit formulae are determined. Finally a relation is discussed to DAD theorems, and a numerical algorithm is given (which has geometric rate of covergence) for determining the minimum information distributions.     

Conditional entropy,entropy density,and strong law of large numbers for generalized controlled tree-indexed Markov chains

In this paper, we first introduces a tree model without degree boundedness restriction namely generalized controlled tree T, which is an extension of some known tree models, such as homogeneous tree model, uniformly bounded degree tree model, controlled tree model, etc. Then some limit properties including strong law of large numbers for generalized controlled tree-indexed non homogeneous Markov chain are obtained. Finally, we establish some entropy density properties, monotonicity of conditional entropy, and entropy properties for generalized controlled tree-indexed Markov chains.     

Monte Carlo comparison of five exponentiality tests using different entropy estimates

The paper studies five entropy tests of exponentiality using five statistics based on different entropy estimates. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for each of the test statistics. By simulation, we compare the power of these five tests for various alternatives and sample sizes.     

基于熵理论的河北省可持续发展水平评价研究

根据2000—2009年国家统计年鉴中河北省的有关数据，选取有代表性的指标，构造评价可持续发展水平的指标体系，并采用熵理论确定各指标的权重，以观察近10年来河北省经济社会可持续发展的具体情况。实证研究结果表明：河北省正逐渐迈向可持续发展的道路,但任重道远。根据省际具体情况，在实证研究的基础上，就河北省经济社会的长期可持续发展提出了若干建议。     

The Complete Exact Null Distribution of Spearman's Rho for n = 12(1)18

Spearman's rank correlation coefficient, Rho, is a widely used nonparametric measure of association. Complete, exact tables of the null distribution are calculated and presented for n = 12 to 18.     

Robust bootstrap estimates in heteroscedastic semi-varying coefficient models and applications in analyzing Australia CPI data

This article deals with the estimation of the parametric component, which is of primary interest, in the heteroscedastic semi-varying coefficient models. Based on the bootstrap technique, we present a procedure for estimating the parameters, which can provide a reliable approximation to the asymptotic distribution of the profile least-square (PLS) estimator. Furthermore, a bootstrap-type estimator of covariance matrix is developed, which is proved to be a consistent estimator of the covariance matrix. Moreover, some simulation experiments are conducted to evaluate the finite sample performance for the proposed methodology. Finally, the Australia CPI dataset is analyzed to demonstrate the application of the methods.     

Ridge Regression and Generalized Maximum Entropy: An improved version of the Ridge–GME parameter estimator

In this article, the Ridge–GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. A serious concern with the visual inspection of the ridge trace to define the supports for the parameters in the Ridge–GME parameter estimator is the misinterpretation of some ridge traces, in particular where some of them are very close to the axes. A simulation study and two empirical applications are used to illustrate the performance of the improved estimator. A MATLAB code is provided as supplementary material.     

A discrete-time risk model with Poisson ARCH claim-number process

Abstract

In this paper, we propose a discrete-time risk model with the claim number following an integer-valued autoregressive conditional heteroscedasticity (ARCH) process with Poisson deviates. In this model, the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the impact of the Poisson ARCH dependence structure on the ruin probability.     

Similar coefficient for cluster of probability density functions

In this article, we propose a new criterion to evaluate the similarity of probability density functions (pdfs). We call this the criterion on similar coefficient of cluster (SCC) and use it as a tool to deal with overlap coefficients of pdfs in normal standard on [0;1]. With the support of the self-update algorithm for determining the suitable number of clusters, SCC then becomes a criterion to establish the corresponding cluster for pdfs. Moreover, some results on determination of SCC in case of two and more than two pdfs as well as relations of different SCCs and other measures are presented. The numerical examples in both synthetic data and real data are given not only to illustrate the suitability of proposed theories and algorithms but also to demonstrate the applicability and innovation of the proposed algorithm.     

Kumaraswamy Marshall-Olkin Exponential distribution

In this paper, a new generalization of the Kumaraswamy distribution namely, the Kumaraswamy Marshall-Olkin Exponential distribution (KwMOE) is introduced and studied. Various properties are explored. The structural analysis includes various aspects such as limiting behaviour, shape properties, moments, quantiles, mean deviation, Renyi entropy, order statistics and stochastic ordering. Some useful characterizations of the family are also obtained. The method of maximum likelihood is used to estimate the model parameters. Monte Carlo simulation study is being conducted. An application to a real data set is presented for illustrative purposes.