A note on the Cauchy-type mixture distributions

An interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property.     

李白的货币思想

货币是应人类商品交换的需要而产生的一种工具.人类创造这种工具的目的在用其为自己的利益服务.货币交换也是一种游戏,人们几乎在开展货币交换时,就在制定相应的游戏规则.李白深刻揭示货币运行的规律,并遵循交换的"游戏" 规则,从多方面利用货币为人类服务:或充分利用货币的使用价值以福利人;或积极发挥货币交换的职能作用以愉悦人;或努力促进货币循环流通的运动以激励人;或深刻揭示货币充当等价商品的本质以沟通人.     

正则图的剖分图的秩

讨论几类正则图的剖分图的邻接矩阵的秩。主要有:圈,路,完全图,完全二部图和多部图,度为3与4的循环图。     

论清末女学

中国正规的女校出现于清朝末年。它的出现提高了中国女性的文化素质 ,为女性参与社会创造了条件。但由于受传统和时代的限制 ,清末女学的产生并不能使广大中国女性走向独立解放的道路     

论新闻报道策划的实践意义

新闻报道策划 在近几年的新闻实践中应用非常广泛。就报道主题、整合信息、沟通受众和发挥媒体整体优 势等方面论述了新闻报道策划的实践意义。     

Correlation Coefficient Revisited

Elementary approaches to prove basic properties of the correlation coefficient are of pedagogical interest. Besides posing another proof, this article gives variations of the proofs already existing in the statistical literature     

First- and Second-order Asymptotics for the Tail Distortion Risk Measure of Extreme Risks

The tail distortion risk measure at level p was first introduced in Zhu and Li (2012 Zhu, L., Li, H. (2012). Tail distortion risk and its asymptotic analysis. Insur. Math. Econ. 51(1):115–121.[Crossref], [Web of Science ®] , [Google Scholar]), where the parameter p ∈ (0, 1) indicates the confidence level. They established first-order asymptotics for this risk measure, as p↑1, for the Fréchet case. In this article, we extend their work by establishing both first-order and second-order asymptotics for the Fréchet, Weibull, and Gumbel cases. Numerical studies are also carried out to examine the accuracy of both asymptotics.     

New Folded Models for the Log-Transformed Norwegian Fire Claim Data

Folded distributions are useful models in statistics. However, not much is known beyond the folded normal distribution introduced in the 1960s. Here, we introduce several new folded distributions. Statistical properties of each distribution are derived. Applications are provided to the Norwegian fire claim data.     

A generalization of Jeffreys' rule for non regular models

ABSTRACT

We propose a generalization of the one-dimensional Jeffreys' rule in order to obtain non informative prior distributions for non regular models, taking into account the comments made by Jeffreys in his article of 1946. These non informatives are parameterization invariant and the Bayesian intervals have good behavior in frequentist inference. In some important cases, we can generate non informative distributions for multi-parameter models with non regular parameters. In non regular models, the Bayesian method offers a satisfactory solution to the inference problem and also avoids the problem that the maximum likelihood estimator has with these models. Finally, we obtain non informative distributions in job-search and deterministic frontier production homogenous models.     

Ban Estimation for Chi-Square Test Criteria in Categorical Data

This expository paper describes some recent work that further develops the theory of BAN estimators and the related chi-scuare test statistics.The extensions are in several directions: (a) the class of regular estimators is broadened by permitting extraneous random elements; (b) more general models are permitted under the constraint equations specification; and (c) BAN estimators are defined for general models combining features of two types of specification.In particular, WLS estimators are shown to be BAN.