Sum,product and ratio of Pareto and gamma variables

The exact distributions of X+Y, X Y and X/(X+Y) are studied when X and Y are independent Pareto and gamma random variables. Applications are discussed, to real problems in clinical trials, computer networks and economics.     

A comparative study of confidence intervals for negative binomial proportion

In this paper, we investigate four existing and three new confidence interval estimators for the negative binomial proportion (i.e., proportion under inverse/negative binomial sampling). An extensive and systematic comparative study among these confidence interval estimators through Monte Carlo simulations is presented. The performance of these confidence intervals are evaluated in terms of their coverage probabilities and expected interval widths. Our simulation studies suggest that the confidence interval estimator based on saddlepoint approximation is more appealing for large coverage levels (e.g., nominal level≤1% ) whereas the score confidence interval estimator is more desirable for those commonly used coverage levels (e.g., nominal level>1% ). We illustrate these confidence interval construction methods with a real data set from a maternal congenital heart disease study.     

On analysis of binary response data in longitudinal factorial studies

Binary data are commonly used as responses to assess the effects of independent variables in longitudinal factorial studies. Such effects can be assessed in terms of the rate difference (RD), the odds ratio (OR), or the rate ratio (RR). Traditionally, the logistic regression seems always a recommended method with statistical comparisons made in terms of the OR. Statistical inference in terms of the RD and RR can then be derived using the delta method. However, this approach is hard to realize when repeated measures occur. To obtain statistical inference in longitudinal factorial studies, the current article shows that the mixed-effects model for repeated measures, the logistic regression for repeated measures, the log-transformed regression for repeated measures, and the rank-based methods are all valid methods that lead to inference in terms of the RD, OR, and RR, respectively. Asymptotic linear relationships between the estimators of the regression coefficients of these models are derived when the weight (working covariance) matrix is an identity matrix. Conditions for the Wald-type tests to be asymptotically equivalent in these models are provided and powers were compared using simulation studies. A phase III clinical trial is used to illustrate the investigated methods with corresponding SAS® code supplied.     

Testing variance components in balanced linear growth curve models

It is well known that the testing of zero variance components is a non-standard problem since the null hypothesis is on the boundary of the parameter space. The usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold because of this null hypothesis. To circumvent this difficulty in balanced linear growth curve models, we introduce an appropriate test statistic and suggest a permutation procedure to approximate its finite-sample distribution. The proposed test alleviates the necessity of any distributional assumptions for the random effects and errors and can easily be applied for testing multiple variance components. Our simulation studies show that the proposed test has Type I error rate close to the nominal level. The power of the proposed test is also compared with the likelihood ratio test in the simulations. An application on data from an orthodontic study is presented and discussed.     

Two non parametric methods for change-point detection in distribution

The change-point detection problem is determining whether a change has taken place. Two non parametric methods based on empirical likelihood and the likelihood ratio are proposed for detecting a change-point problem in distributions for independent observations. Numerical studies are carried out to evaluate the performance of the proposed methods. The simulation results demonstrate that the proposed methods are robust, that is, they perform well regardless of whether the observations are from the same distribution family.     

Inverse gaussian accelerated test models based on cumulative damage

The failure of a system under environmental stress often can be described by an accelerated test model which incorporates the environmental variable L. Here, the failure of such a system at environmental level L is modeled as the first passage of accumulated damage to a critical threshold value. Assuming a discrete additive damage model leads to a Birnbaum–Saunders-type distribution for the failure time which can be closely approximated by an inverse Gaussian-type model. However, if a continuous damage model based on a Gaussian process is assumed, a more general family of inverse Gaussian accelerated test models is obtained. Three sets of failure data are discussed to illustrate the usefulness of this general family.     

New goodness of fit tests for the Cauchy distribution

Some goodness-of-fit procedures for the Cauchy distribution are presented. The power comparisons indicate that the new tests possess good performances among the competitors, especially against symmetric alternatives. A financial data set is analyzed for illustration.     

A lost family-planning regime in eighteenth-century Ceylon

Based on Dutch colonial registers (thombos), this paper reconstructs fertility for two districts in Ceylon, 1756–68. It overcomes challenges in data quality by establishing the outer bounds of plausible estimates in a series of scenarios. Among these, total fertility rates (TFRs) averaged 5.5 in one district, but only 2.7 in the other. These figures exclude the victims of infanticide, a custom noted in European travelogues between about 1660 and 1820. Sex ratios among children differed depending on the number of older siblings, and overall, 27?per cent of girls are missing in one district and 57?per cent in the other. There was little significant variation either in the TFR or the sex ratio by socio-economic status, suggesting that poverty was not a key factor in motivating infanticides. Instead, we argue that at least parts of Ceylon had a forward-looking culture of family planning in the eighteenth century, which was lost in subsequent decades.     

欧洲债务危机的主要成因分析

肇始于希腊的欧洲债务危机到目前为止都没有停息的迹象,甚至还呈蔓延之势。欧洲债务危机爆发的直接原因是在金融危机的背景下,政府支出规模持续扩大,导致财政赤字居高不下,最终使得国债规模超过政府的偿还能力,出现明显的违约可能性。同时,国际竞争力不足,导致出口受阻,使得资金问题更加严重。从更深层次看,产业结构不合理,经济发展速度缓慢,过低的投资率和储蓄率及过高的储蓄投资转化率,都是导致欧债危机的重要原因。     

天然岩芯化学驱采收率机理的一些认识

用牛顿流体驱替一定的均质多孔介质系统结果显示，驱油效率由驱替液的毛管数决定。用化学液驱替天然岩芯时，除毛管数以外，还有很多其他因素影响驱油效率。天然岩芯，即使在宏观上是均匀的，在微观上也不均匀；驱替时所得到的效率一般被称为驱油效率，实质上是微观波及效率和驱油效率的乘积。牛顿流体没有弹性，驱替时，体系的润湿性不发生变化，不出现渗吸作用，不形成乳液，孔隙的几何形状不发生变化。但是，用化学液驱替天然岩芯时，由于化学液为粘弹性，体系有润湿性的改变，会出现乳化现象，渗吸作用也会出现。上述因素都会影响驱油效率，尤其是当多种因素同时作用时。分析了极限采收率和经济采收率的区别。很多文章都论述极限采收率，但经济采收率对油田的作用更大。化学驱应考虑上述因素，这对设计、开发、筛选化学剂以及确定驱油体系会是有益的，将深化我们对化学驱机理的认识，促进这方面更深入的研究。