A spatial scan statistic for survival data based on generalized life distribution

ABSTRACT

For many years, detection of clusters has been of great public health interest and widely studied. Several methods have been developed to detect clusters and their performance has been evaluated in various contexts. Spatial scan statistics are widely used for geographical cluster detection and inference. Different types of discrete or continuous data can be analyzed using spatial scan statistics for Bernoulli, Poisson, ordinal, exponential, and normal models. In this paper, we propose a scan statistic for survival data which is based on generalized life distribution model that provides three important life distributions, viz. Weibull, exponential, and Rayleigh. The proposed method is applied to the survival data of tuberculosis patients in Nainital district of Uttarakhand, India, for the year 2004–05. The Monte Carlo simulation studies reveal that the proposed method performs well for different survival distributions.     

A comparison of risk transfer strategies for a portfolio of life annuities based on RORAC

This paper aims to compare different reinsurance arrangements in order to reduce the longevity and financial risk originated by a life insurer while managing a portfolio of annuities policies. Linear and nonlinear reinsurance strategies as well as swap like agreements are evaluated via a discrete-time actuarial risk model. Specifically, longevity dynamics are represented by Lee–Carter type models, while interest rate is modeled by Cox–Ingersoll–Ross model. The reinsurance strategies effectiveness is evaluated according to the Return on Risk Adjusted Capital under a ruin probability constrain.     

Optimal investment and life insurance strategies in a mixed jump-diffusion framework

Abstract

This article investigates an optimal investment and life insurance strategies in a mixed jump-diffusion framework. The individual life insurance policyholder who has CRRA preferences. The market consists of riskless asset, a zero-coupon bond, a stock and life insurance. The instantaneous interest rate is modeled as the O-U model, while a zero-coupon bond with credit risk follows a BSDE and a risky asset be driven by MJD-fBm model. The problem is solved by the mixed jump diffusion fractional HJB SDE which satisfied the admissible strategy, then the closed form solution and optimal strategies are derived and the simulation of the various parameters are also given.     

Valuing equity-indexed annuities with icicled barrier options

Inspired by the recent popularity of autocallable structured products, this paper intends to enhance equity-indexed annuities (EIAs) by introducing a new class of barrier options, termed icicled barrier options. The new class of options has a vertical (icicled) barrier along with the horizontal one of the ordinary barrier options, which may act as an additional knock-in or knock-out trigger. To improve the crediting method of EIAs, we propose a new EIA design, termed autocallable EIA, with payoff structure similar to the autocallable products except for the minimum guarantee, and further investigate the possibility of embedding various icicled barrier options into the plain point-to-point or the ratchet EIAs. Explicit pricing formulas for the proposed EIAs and the icicled barrier options are obtained under the Black–Scholes model. To the purpose, we derive the joint distribution of the logarithmic returns at the icicled time and the maturity, and their running maximum. As an application of the well-known reflection principle, the derivation itself is an interesting probability problem and the joint distribution plays a key role in the subsequent pricing stage. Our option pricing result can be easily transferred to EIAs or other equity-linked products. The pricing formulas for the EIAs and the options are illustrated through numerical examples.     

Reliability statistical analysis about products of Birnbaum–Saunders fatigue life distribution for life test and progressive stress accelerated life test

Birnbaum–Saunders fatigue life distribution is an important failure model in the probability physical methods. It is more suitable for describing the life rules of fatigue failure products than common life distributions such as Weibull distribution and lognormal distribution. Besides, it is mainly applied to analytical research about fatigue failure and degradation failure of electronic product performance. The characteristic properties such as numerical characteristics and image features of density function and failure rate function are studied for generalized BS fatigue life distribution GBS(α, β, m) in this paper. Then the point estimates and approximate interval estimates of parameters are proposed for generalized BS fatigue life distribution GBS(α, β, m), and the precision of estimates are investigated by Monte Carlo simulations. Finally, when the scale parameter satisfies inverse power law model, the failure distribution model is given for the products of two-parameter BS fatigue life distribution BS(α, β) under progressive stress accelerated life test according to the time conversion idea of famous Nelson assumption, and then the points estimates of parameters are given.     

Optimal investment-consumption and life insurance with capital constraints

Abstract

The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal strategy and the optimal martingale measure and we obtain the explicit solutions for the power utility functions.     

Pricing and hedging equity-indexed annuities via local risk-minimization

Lin et al. (2009) employed the Esscher transform method to price equity-indexed annuities (EIAs) when the dynamic of the market value of a reference asset was driven by a generalized geometric Brownian motion model with regime-switching. Some rare events (release of an unexpected economic figure, major political changes or even a natural disaster in a major economy) can lead to brusque variations in asset prices, and hence we sometimes need to consider jump models. This paper extends the model and analysis in Lin et al. (2009). Specifically, we assume that the financial market has a regime-switching jump-diffusion model, under which we price the point-to-point, the Asian-end, the high water mark and the annual reset EIAs by exploiting the local risk-minimization approach. The effects of the model parameters on the EIAs pricing are illustrated through numerical experiments. Meanwhile, we present the locally risk-minimizing hedging strategies for EIAs.     

Performance of standard imputation methods for missing quality of life data as covariate in survival analysis based on simulations from the International Breast Cancer Study Group Trials VI and VII*

Abstract

Imputation methods for missing data on a time-dependent variable within time-dependent Cox models are investigated in a simulation study. Quality of life (QoL) assessments were removed from the complete simulated datasets, which have a positive relationship between QoL and disease-free survival (DFS) and delayed chemotherapy and DFS, by missing at random and missing not at random (MNAR) mechanisms. Standard imputation methods were applied before analysis. Method performance was influenced by missing data mechanism, with one exception for simple imputation. The greatest bias occurred under MNAR and large effect sizes. It is important to carefully investigate the missing data mechanism.     

Covariate effect on the life expectancy and percentile residual life functions under the proportional hazards and the accelerated life models

The present paper is concerned with statistical models for the dependence of survival time or time to occurrence of an event, such as time to tumor, on a vector X of covariates or prognostic variables such as age, sex, blood pressure, length of exposure to a toxic material, etc., measured on a group of individuals in biomedical investigations. It is assumed that the covariates influence the distribution of time to tumor only through a linear predictor μ =β^′X.

The object of our paper is to investigate the effect due to the covariates on the Life Expectancy and the Percentile Residual Life (PRL) function of a family of organisms under the proportional hazards and the accelerated life models. The key result is that the families of survival distributions under these models have the 'setting the clock back to zero' property if the family of baseline survival distributions does. This property is a generalization of the lack of memory property of the exponential distribution. Simple examples of the members of this family are the linear hazard exponential, Pareto and Gompertz life distributions.

As a simple application of the main results obtained in the present paper, we have considered a stochastic survival model recently proposed by Chiang and Conforti (1989) for the time-to-tumor distribution in the context of a large-scale serial sacrifice experiment by the National Center of Toxicological Research (NCTR). This involves some mice that were fed 2-AAF from infancy and those that developed bladder and/or liver neoplasms, see Farmer et al (1980). It is shown that their stochastic model for tumor incidence intensity at time t leads to a family of survival models that has the setting the clock back to zero property. The survival functions and the effect of the vector X of covariates on the PRL and the tumor-free life expectancies are evaluated for the proportional hazards and accelerated life models.     

Jackknife empirical likelihood test for mean residual life functions

Mean residual life (MRL) function is an important function in survival analysis which describes the expected remaining life given survival to a certain age. In this article, we propose a non parametric method based on jackknife empirical likelihood through a U-statistic to test the equality of two mean residual functions. The asymptotic distribution of the test statistic has been derived. Simulations are conducted to illustrate the performance of the proposed test under different distributional assumptions and compare with some existing method. The proposed method is then applied to two real datasets.     

Valuation of contingent claims with stochastic interest rate and mortality driven by Lévy processes

Abstract

In this paper, we consider a model with stochastic interest rate and stochastic mortality, which is driven by a Lévy process. Under the assumption that the stochastic mortality and interest rate are dependent, we discuss the valuation of life insurance contracts. Employing the method of change of measure together with the Bayes’ rule, we present the pricing formulas in closed form for the survival and death benefit models. Finally, numerical experiments illustrate the effects of some parameters.     

Classical estimation of hazard rate and mean residual life functions of Pareto distribution

Abstract

In this paper we find the maximum likelihood estimates (MLEs) of hazard rate and mean residual life functions (MRLF) of Pareto distribution, their asymptotic non degenerate distribution, exact distribution and moments. We also discuss the uniformly minimum variance unbiased estimate (UMVUE) of hazard rate function and MRLF. Finally, two numerical examples with simulated data and real data set, are presented to illustrate the proposed estimates.     

养老保险个人账户参数设定错误与纠正

我国基本养老保险采取统账结合的制度模式。其中，个人账户采用记账方式建立了参保缴费与养老待遇之间的直接联系。理论上，公平和长期可持续的个人账户模式在记账利率、计发系数、余额继承等方面应遵循精算原则，但我国的个人账户参数设定存在不少违背精算公平和精算平衡原则的错误。本文结合国际经验，在剖析我国养老保险个人账户参数设定错误的基础上，基于精算平衡原理，探讨参数设定方法，检验纠正方案对制度精算公平和精算平衡性的效果，最后提出参数改革的具体建议。主要结论是：个人账户的记账利率应该是制度的内含回报率；名义账户的记账利率不是银行存款利率，而应随缴费工资增长率、人口预期寿命的变动等定期调整；养老金计发系数应基于动态生命表、养老金调整指数和个人账户内含回报率的变动而调整。由此确定的参数纠正方案将有效改善制度的精算公平与精算平衡性。因而建议我国基本养老保险个人账户应尽早明确现收现付的筹资模式和账户余额的权益归属，采用动态的记账利率和计发月数，引入自动平衡机制，实现制度的长期精算平衡。     

Estimation of monotone bivariate quantile residual life

The bivariate quantile residual life function can play an important role in statistical reliability and survival analysis. In many situations assuming a decreasing form for it is recommended. Here, we propose a new non-parametric estimator of this measure under such restriction. It has been shown that the new estimator is consistent and, with proper normalization, weakly converges to a bivariate Gaussian process. A simulation study shows that the proposed estimator is an alternative to the unrestricted estimator when the bivariate quantile residual life is decreasing. Finally, the new estimators are applied to two real data sets.     

On the mean residual life function of a mixture in reliability studies

In reliability studies, the additional life time given that a component has survived until time t is called the Mean residual life function (MRLF). This MRLF determines the distribution function uniquely. There exist many life testing situations which can be best described as mixtures of distributions. In this paper we have considered the general MRLF and have developed a method of obtaining the mixing distribution when the original distribution is exponential. Some examples are discussed, in one of which Morrison’s (1978) result is obtained as a special case.     

Nonparametric inference on mean residual life function with length-biased right-censored data

Abstract

In survival or reliability studies, the mean residual life (MRL) function is an important characteristic in understanding the survival or ageing process. In this article, we consider the problem of nonparametric MRL function estimation with length-biased right-censored data. Two nonparametric estimators of the MRL are proposed and their weak convergence is presented. In order to evaluate the performance of these estimators, small Monte Carlo simulations are carried out. Results show that the proposed estimators work well especially when the sample size is small and their calculations are simple. Finally, a real data example is provided.     

A Bayesian approach for misclassified ordinal response data

ABSTRACT

Motivated by a longitudinal oral health study, the Signal-Tandmobiel^® study, a Bayesian approach has been developed to model misclassified ordinal response data. Two regression models have been considered to incorporate misclassification in the categorical response. Specifically, probit and logit models have been developed. The computational difficulties have been avoided by using data augmentation. This idea is exploited to derive efficient Markov chain Monte Carlo methods. Although the method is proposed for ordered categories, it can also be implemented for unordered ones in a simple way. The model performance is shown through a simulation-based example and the analysis of the motivating study.     

“做实做小”个人账户对个人养老金水平的影响

 本文引入养老保险金记账利率和工资增长率，测算了在不同初始缴费工资和缴费年限条件下实施“做实做小”个人账户政策对参保人养老金水平的影响。通过分析得出：1.政策调整后，养老金给付结构较调整前更能体现缴费积累与养老金水平的内在经济联系； 2.政策调整后个人养老金水平普遍不如政策调整前的水平，政策调整后养老金水平高于政策调整前均出现在缴费年限较长以及初始缴费工资较高的情况下；3.政策调整对不同的参保人影响不同。政策调整加大了低初始缴费工资人群的生活压力；拉大了男、女职工退休养老金的差距，不利于当前社会男女平等和贫富分化问题的解决。     

Random balanced resampling: A new method for estimating variance components in unbalanced designs

Variance components in factorial designs with balanced data are commonly estimated by equating mean squares to expected mean squares. For unbalanced data, the usual extensions of this approach are the Henderson methods, which require formulas that are rather involved. Alternatively, maximum likelihood estimation based on normality has been proposed. Although the algorithm for maximum likelihood is computationally complex, programs exist in some statistical packages. This article introduces a simpler method, that of creating a balanced data set by resampling from the original one. Revised formulas for expected mean squares are presented for the two-way case; they are easily generalized to larger factorial designs. The results of a number of simulation studies indicate that, in certain types of designs, the proposed method has performance advantages over both the Henderson Method I and maximum likelihood estimators.