Estimation and testing procedures for the reliability functions of a general class of distributions

We consider here the general class of distributions proposed by Sankaran and Gupta (2005) by zeroing in on two measures of reliability, R(t) = P(X > t) and P = P(X > Y). Thereafter, we develop point estimation for R(t) and ‘P’ and develop uniformly minimum variance unbiased estimators (UMVUES). Then we derive testing procedures for the hypotheses related to different parametric functions. Finally, we compare the results using the Monte Carlo simulation method. Using real data set, we illustrate the procedure clearly.     

Tables of the cumulative non-central chi-square distribution - part l 1

The cumulative non-central chi-square distribution is tabulated for all combinations of values of λ=0(.01) 1.0 (0.2) 3.0 (0.5) 5.0 (1.0) 34.0, ν = l (1) 30 (2) 50 (5) 100 and y= 0.0l (0.01) 0.1 (0,1) 1.0 (0.2) 3.0 (0.5) 10.0 (1.0) 30.0 (2.0) 50.0 (5.0) 165.0. The computations have been correctly rounded to five decimal places. Also, there is a discussion about the error involved in the computations. Furthermore, there is a discussion about possible interpolation in the table using the Lagrange's method.     

Adaptive Mixtures of Regressions: Improving Predictive Inference when Population has Changed

The present work investigates the estimation of regression mixtures when population has changed between the training and the prediction stages. Two approaches are proposed: a parametric approach modeling the relationship between dependent variables of both populations, and a Bayesian approach in which the priors on the prediction population depend on the mixture regression parameters of the training population. The relevance of both approaches is illustrated on simulations and on an environmental dataset.     

The application of the durbin-watson test to the dynamic regression model under normal and non-normal errors

Until recently, a difficulty with applying the Durbin-Watson (DW) test to the dynamic linear regression model has been the lack of appropriate critical values. Inder (1986) used a modified small-disturbance distribution (SDD) to find approximate critical values. King and Wu (1991) showed that the exact SDD of the DW statistic is equivalent to the distribution of the DW statistic from the regression with the lagged dependent variables replaced by their means. Unfortunately, these means are unknown although they could be estimated by the actual variable values. This provides a justification for using the exact critical values of the DW statistic from the regression with the lagged dependent variables treated as non-stochastic regressors. Extensive Monte Carlo experiments are reported in this paper. They show that this approach leads to reasonably accurate critical values, particularly when two lags of the dependent variable are present. Robustness to non-normality is also investigated.     

基于整合治愈率模型的信贷违约时点预测

传统信用评分方法主要利用统计分类方法,只能预测借款人是否会发生违约,但不能预测违约发生的时点。治愈率模型是二分类和生存分析的混合模型,不仅可以预测是否会发生违约,而且可以预测违约发生的时点,比传统二分类方法可以提供更多的信息。另外,随着大数据的发展,数据源越来越多,针对相同或者相似任务,可以收集到多个数据集,本文提出了融合多源数据的整合治愈率模型,可以对多个数据集同时建模和估计参数,通过复合惩罚函数进行组间和组内双层变量选择,并通过促进两个子模型回归系数符号相同,提高模型的可解释性。通过数值模拟发现,所提方法在变量选择和参数估计上均有明显优势。最后,将所提方法应用于信用贷款的违约时点预测中,模型表现良好。     

A precise estimator for the log-normal mean

The log-normal distribution is frequently encountered in applications. The uniformly minimum variance unbiased (UMVU) estimator for the log-normal mean is given explicitly by a formula found by Finney in 1941. In contrast to this the most commonly used estimator for a log-normal mean is the sample mean. This is possibly due to the complexity of the formula given by Finney. A modified maximum likelihood estimator which approximates the UMVU estimator is derived here. It is sufficiently simple to be implemented in elementary spreadsheet applications. An elementary approximate formula for the root-mean-square error of the suggested estimator and the UMVU estimator is presented. The suggested estimator is compared with the sample mean, the maximum likelihood, and the UMVU estimators by Monte Carlo simulation in terms of root-mean-square error.     

论管理科学领域的时间关系

管理科学领域所涉及的时间关系,构造了以时刻关系为基础的完备时间关系集合Г,这些关系为管理科学领域的时间关系的应用提供了一个理论依据和时间表达参考规范。     

Weaving new retail and consumer landscapes in the Scottish Borders

New retail locations and formats and changing consumer capabilities and behaviours (including “switching”) have encouraged “outshopping” from rural to urban areas. Rural areas have been suffering from a decline in the provision of services, including retailing. One “solution” has been the strengthening of market towns in rural areas by the development of new major retail stores. The effects of this are perhaps not fully understood, particularly where the rural area comprises a network of towns rather than a single centre. Three comparable consumer surveys (1988, 1998, 2004) of shopping behaviour in the Scottish Borders are analysed. Consumer place and store switching data are used to examine the impact of new retail opportunities on shopping patterns. Two different switching strands are identified: clawback and redistribution. Redistribution within the rural network is a new finding.     

Consumer attitudes towards switching supplier in three deregulated markets

The efficiency of deregulated markets is jeopardized by consumers failing to switch supplier to the extent that would be beneficial to them. In order to disentangle the determinants of failures to switch, the present study investigates consumers’ motives for negative attitudes towards switching in the deregulated Swedish markets for electricity, landline telecom, and home insurance. Based on the results of a mail survey of a random sample of 458 household consumers, reliable measures were constructed of attitude towards switching supplier, loyalty to the incumbent, information search costs to compare suppliers, and expected economic benefits from switching. A negative attitude towards switching supplier was shown to increase with loyalty, increase with information search costs and decrease with expected economic benefits. Attitude towards switching was more negative in the electricity market than in the other markets and more negative in the landline telecom market than in the home insurance market. The differences between markets were accounted for by differences in loyalty, information search costs, and expected economic benefits.     

Response adaptive designs that incorporate switching costs and constraints

This paper examines the design and performance of sequential experiments where extensive switching is undesirable. Given an objective function to optimize by sampling between Bernoulli populations, two different models are considered. The constraint model restricts the maximum number of switches possible, while the cost model introduces a charge for each switch. Optimal allocation procedures and a new “hyperopic” procedure are discussed and their behavior examined. For the cost model, if one views the costs as control variables then the optimal allocation procedures yield the optimal tradeoff of expected switches vs. expected value of the objective function.