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.     

Flexible simulation of competing risks data following prespecified subdistribution hazards

In recent years different approaches for the analysis of time-to-event data in the presence of competing risks, i.e. when subjects can fail from one of two or more mutually exclusive types of event, were introduced. Different approaches for the analysis of competing risks data, focusing either on cause-specific or subdistribution hazard rates, were presented in statistical literature. Many new approaches use complicated weighting techniques or resampling methods, not allowing an analytical evaluation of these methods. Simulation studies often replace analytical comparisons, since they can be performed more easily and allow investigation of non-standard scenarios. For adequate simulation studies the generation of appropriate random numbers is essential. We present an approach to generate competing risks data following flexible prespecified subdistribution hazards. Event times and types are simulated using possibly time-dependent cause-specific hazards, chosen in a way that the generated data will follow the desired subdistribution hazards or hazard ratios, respectively.     

Dividend barrier and ruin problems for a risk model with delayed claims

In this paper, a compound Poisson risk model in the presence of a constant dividend barrier is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and and the time of delay for the claim is assumed to be random. A system of integro-differential equations with certain boundary conditions for the expected discounted penalty function is derived. We show that its solution can be expressed as the solution to the expected discounted penalty function in the same risk model with the absence of a barrier plus a linear combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Using systems of integro-differential equations for the moment-generating function as well as for the arbitrary moments of the sum of discounted dividend payments until ruin, a matrix version of the dividends–penalty type relationship is derived. We also prove that ruin is certain under constant dividend barrier strategy. The closed form expressions are given when the claim amounts from both classes are exponentially distributed. Finally, a numerical example is presented to illustrate the solution procedure.     

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.     

On additive-multiplicative hazards model

In survival analysis and reliability theory, a fundamental problem is the study of lifetime properties of a live organism or system. In this regard, there have been considered and studied several models based on different concepts of ageing such as hazard rate and mean residual life. In this paper, we consider an additive-multiplicative hazard model (AMHM) and study some reliability and ageing properties of the proposed model. We then specify the bivariate models whose conditionals satisfy AMHM. Several properties of the proposed bivariate model are investigated and adequacy of the model is evaluated based on a real data set.     

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。     

The estimation of treatment effect for the censored bivariate data under the univariate censoring

This paper establishes a nonparametric estimator for the treatment effect on censored bivariate data under unvariate censoring. This proposed estimator is based on the one from Lin and Ying(1993)'s nonparametric bivariate survival function estimator, which is itself a generalized version of Park and Park(1995)' quantile estimator. A Bahadur type representation of quantile functions were obtained from the marginal survival distribution estimator of Lin and Ying' model. The asymptotic property of this estimator is shown below and the simulation studies are also given     

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varian's asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.