Exponentiality Test Based on the Progressive Type II Censoring via Cumulative Entropy

In this article, we use cumulative residual Kullback-Leibler information (CRKL) and cumulative Kullback-Leibler information (CKL) to construct two goodness-of-fit test statistics for testing exponentiality with progressively Type-II censored data. The power of the proposed tests are compared with the power of goodness-of-fit test for exponentiality introduced by Balakrishnan et al. (2007 Balakrishnan, N., Habibi Rad, A., Arghami, N.R. (2007). Testing exponentiality based on Kullback-Leibler information with progressively type-II censored data. IEEE Transactions on Reliability 56(2):301–307.[Crossref], [Web of Science ®] , [Google Scholar]). We show that when the hazard function of the alternative is monotone decreasing, the test based on CRKL has higher power and when the hazard function of the alternative is non-monotone, the test based on CKL has higher power. But, when it is monotone increasing the power difference between test based on CKL and their proposed test is not so remarkable. The use of the proposed tests is shown in an illustrative example.     

Probability Generating Function Based Jeffrey's Divergence for Statistical Inference

Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test.     

谈弗·雷·利维斯小说批评中的非个性化原则

非个性化是利维斯衡量其伟大小说和小说家的重要尺度.通过时这一尺度的诠释来捕捉和说明利维斯评价标准的实质,推敲和体味这一标准在其重要评价中所具有的丰富意蕴,这对于我们正确理解和评价利维斯的批评事业无疑是至关重要的.     

马克思主义理论课的教学改革探析

结合新课程方案的特点,指出今后马克思主义理论课程的教学方式和考核方式改革的基本思路应该是:在有效利用传统的课堂讲授法的基础上,积极采取课堂讨论法、案例教学法、多媒体教学法等多种教学辅助方式,进一步完善多元化的考试制度。     

Designing and integrating composite networks for monitoring multivariate gaussian pollution fields

Networks of ambient monitoring stations are used to monitor environmental pollution fields such as those for acid rain and air pollution. Such stations provide regular measurements of pollutant concentrations. The networks are established for a variety of purposes at various times so often several stations measuring different subsets of pollutant concentrations can be found in compact geographical regions. The problem of statistically combining these disparate information sources into a single 'network' then arises. Capitalizing on the efficiencies so achieved can then lead to the secondary problem of extending this network. The subject of this paper is a set of 31 air pollution monitoring stations in southern Ontario. Each of these regularly measures a particular subset of ionic sulphate, sulphite, nitrite and ozone. However, this subset varies from station to station. For example only two stations measure all four. Some measure just one. We describe a Bayesian framework for integrating the measurements of these stations to yield a spatial predictive distribution for unmonitored sites and unmeasured concentrations at existing stations. Furthermore we show how this network can be extended by using an entropy maximization criterion. The methods assume that the multivariate response field being measured has a joint Gaussian distribution conditional on its mean and covariance function. A conjugate prior is used for these parameters, some of its hyperparameters being fitted empirically.     

Factors influencing Soay sheep survival

We present a survival analysis of Soay sheep mark recapture and recovery data. Unlike previous conditional analyses, it is not necessary to assume equality of recovery and recapture probabilities; instead these are estimated by maximum likelihood. Male and female sheep are treated separately, with the higher numbers and survival probabilities of the females resulting in a more complex model than that used for the males. In both cases, however, age and time aspects need to be included and there is a strong indication of a reduction in survival for sheep aged 7 years or more. Time variation in survival is related to the size of the population and selected weather variables, by using logistic regression. The size of the population significantly affects the survival probabilities of male and female lambs, and of female sheep aged 7 or more years. March rainfall and a measure of the North Atlantic oscillation are found to influence survival significantly for all age groups considered, for both males and females. Either of these weather variables can be used in a model. Several phenotypic and genotypic individual covariates are also fitted. The only covariate which is found to influence survival significantly is the type of horn of first-year female sheep. There is a substantial variation in the recovery probabilities over time, reflecting in part the increased effort when a population crash was expected. The goodness of fit of the model is checked by using graphical procedures.     

Decision Making in `Random in a Broad Sense' Environments

It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.     

Confidence intervals based on the deviance statistic for the hyperparameters in state space models

The main objective of this work is to evaluate the performance of confidence intervals, built using the deviance statistic, for the hyperparameters of state space models. The first procedure is a marginal approximation to confidence regions, based on the likelihood test, and the second one is based on the signed root deviance profile. Those methods are computationally efficient and are not affected by problems such as intervals with limits outside the parameter space, which can be the case when the focus is on the variances of the errors. The procedures are compared to the usual approaches existing in the literature, which includes the method based on the asymptotic distribution of the maximum likelihood estimator, as well as bootstrap confidence intervals. The comparison is performed via a Monte Carlo study, in order to establish empirically the advantages and disadvantages of each method. The results show that the methods based on the deviance statistic possess a better coverage rate than the asymptotic and bootstrap procedures.     

A volume based approach to establish B-spline based expressions for density functions and its application to progressive hybrid censoring

We propose an approach to determine the distribution of particular linear combinations of hybrid censored order statistics which is based on the calculation of volumes of polytopes. For this purpose, we establish efficient and compact volume formulas in terms of B-splines. Further, we illustrate our approach for ten different progressive hybrid censoring schemes under an exponential assumption.     

Quantifying the similarity of 2D images using edge pixels: an application to the forensic comparison of footwear impressions

We propose a novel method to quantify the similarity between an impression (Q) from an unknown source and a test impression (K) from a known source. Using the property of geometrical congruence in the impressions, the degree of correspondence is quantified using ideas from graph theory and maximum clique (MC). The algorithm uses the x and y coordinates of the edges in the images as the data. We focus on local areas in Q and the corresponding regions in K and extract features for comparison. Using pairs of images with known origin, we train a random forest to classify pairs into mates and non-mates. We collected impressions from 60 pairs of shoes of the same brand and model, worn over six months. Using a different set of very similar shoes, we evaluated the performance of the algorithm in terms of the accuracy with which it correctly classified images into source classes. Using classification error rates and ROC curves, we compare the proposed method to other algorithms in the literature and show that for these data, our method shows good classification performance relative to other methods. The algorithm can be implemented with the R package shoeprintr.