Inferences on the Means of Two Log-Normal Distributions: A Computational Approach Test

In this article, we propose a novel approach for testing the equality of two log-normal populations using a computational approach test (CAT) that does not require explicit knowledge of the sampling distribution of the test statistic. Simulation studies demonstrate that the proposed approach can perform hypothesis testing with satisfying actual size even at small sample sizes. Overall, it is superior to other existing methods. Also, a CAT is proposed for testing about reliability of two log-normal populations when the means are the same. Simulations show that the actual size of this new approach is close to nominal level and better than the score test. At the end, the proposed methods are illustrated using two examples.     

巴渝古崖居的空间分布与景观特征

巴渝古崖居的分布与地理、地质、交通等诸多因素有关，以成渝交通要道、长江干流和支流为线，串起沿途各个点，由线成面，呈现出渝西、渝东北两头集中、整体北多南少的分布特征。巴渝古崖居大多开凿于明清晚期，这一时期巴渝许多地区战乱频繁、匪患猖獗。古崖居的集中分布与这些地区相吻合，从侧面印证了巴渝古崖居的空间分布特征。巴渝古崖居的广泛开凿体现了古人高超的建筑艺术以及社会历史文化的变迁。     

A new generalized Weibull distribution in income economic inequality curves

Researchers have been developing various extensions and modified forms of the Weibull distribution to enhance its capability for modeling and fitting different data sets. In this note, we investigate the potential usefulness of the new modification to the standard Weibull distribution called odd Weibull distribution in income economic inequality studies. Some mathematical and statistical properties of this model are proposed. We obtain explicit expressions for the first incomplete moment, quantile function, Lorenz and Zenga curves and related inequality indices. In addition to the well-known stochastic order based on Lorenz curve, the stochastic order based on Zenga curve is considered. Since the new generalized Weibull distribution seems to be suitable to model wealth, financial, actuarial and especially income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. Also, the estimation of parameters by maximum likelihood and moment methods is discussed. Finally, this distribution has been fitted to United States and Austrian income data sets and has been found to fit remarkably well in compare with the other widely used income models.     

Cognitive abilities,self-efficacy,and financial behavior

This paper investigates the effect of cognitive abilities on financial behavior among older adults. Using the U.S. Health and Retirement Study, I find that cognitive abilities significantly affect financial behavior through two channels: ability and self-efficacy. People with higher cognition scores achieve better financial outcomes. This positive association is especially strong in tasks having high demand of cognitive abilities, which confirms the ability channel of the cognitive ability effect. In addition, there is evidence for the self-efficacy channel as a secondary source of cognitive influence. Lower cognitive abilities decrease people’s sense of self-efficacy, which, in turn, significantly decreases financial management efficiency. The findings have important policy implications, specifically that more effort is needed to assist the growing older population through the cognitive aging process and that noncognitive skills, as a secondary source of influence, also warrant attention.     

Does a universal non-contributory social pension make sense for rural China?

China’s pension reform during the past three decades has allowed a majority of China’s population to be covered by a pension scheme. Of particular note has been the New Rural Pension Scheme (NRPS), a voluntary programme introduced starting in 2009. One goal of our analysis is to assess that pension scheme, using a variety of sources of information including data drawn from recent (2013 and 2015) nationwide China Health and Retirement Longitudinal Surveys (CHARLS). Our analysis involves an exploration of differences between the generosity and structure of the NRPS and other pension schemes currently in place. We also explore the feasibility of reforming the current “quasi-social pension” component of the NRPS by substituting a universal non-contributory social pension pillar. In connection with our assessment of the NRPS, we note the unusually low benefit levels for rural China.     

On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

Analyzing multiple vector autoregressions through matrix-variate normal distribution with two covariance matrices

Abstract

This article proposes a new approach to analyze multiple vector autoregressive (VAR) models that render us a newly constructed matrix autoregressive (MtAR) model based on a matrix-variate normal distribution with two covariance matrices. The MtAR is a generalization of VAR models where the two covariance matrices allow the extension of MtAR to a structural MtAR analysis. The proposed MtAR can also incorporate different lag orders across VAR systems that provide more flexibility to the model. The estimation results from a simulation study and an empirical study on macroeconomic application show favorable performance of our proposed models and method.     

The quantile-based flattened logistic distribution: Some properties and applications

In this paper, the quantile-based flattened logistic distribution has been studied. Some classical and quantile-based properties of the distribution have been obtained. Closed form expressions of L-moments, L-moment ratios and expectation of order statistics of the distribution have been obtained. A quantile-based analysis concerning the method of matching L-moments estimation is employed to estimate the parameters of the proposed model. We further derive the asymptotic variance–covariance matrix of the matching L-Moments estimators of the proposed model. Finally, we apply the proposed model to simulated as well as two real life datasets and compare the fit with the logistic distribution.     

Beyond tail median and conditional tail expectation: Extreme risk estimation using tail Lp-optimization

The conditional tail expectation (CTE) is an indicator of tail behavior that takes into account both the frequency and magnitude of a tail event. However, the asymptotic normality of its empirical estimator requires that the underlying distribution possess a finite variance; this can be a strong restriction in actuarial and financial applications. A valuable alternative is the median shortfall (MS), although it only gives information about the frequency of a tail event. We construct a class of tail L^p-medians encompassing the MS and CTE. For p in (1,2), a tail L^p-median depends on both the frequency and magnitude of tail events, and its empirical estimator is, within the range of the data, asymptotically normal under a condition weaker than a finite variance. We extrapolate this estimator and another technique to extreme levels using the heavy-tailed framework. The estimators are showcased on a simulation study and on real fire insurance data.