The finite-time ruin probability of a discrete-time risk model with GARCH discounted factors and dependent risks

The finite-time ruin probability of a discrete-time risk model with dependent stochastic discount factors and dependent insurance and financial risks is investigated in this paper. Assume that the stochastic discount factors follow a GARCH process and the one-period insurance and financial risks form a sequence of independent and identically distributed random pairs, which are the copies of a random pair with a bivariate Sarmanov dependent distribution. When the common distribution of claim-sizes is heavy-tailed, we establish an asymptotic estimate for the finite-time ruin probability. Applying the result to a special case, we also get conservative asymptotic bounds. A numerical simulation is given at the end of the paper.     

印度瑜伽行派唯识学缘起思想之特质

印度瑜伽行派唯识学的缘起理论具有四个与印度佛教其他派别缘起思想不共的特质,即缘起的因果平等性、缘起的唯心性、缘起的俱时性、缘起的整体性,不论有为依唯识思想还是无为依唯识思想在这方面皆是如此。但由于唯识学的此二分型在本体论方面相异,对此四特质的说明自然会有所不同。     

On Generalized Binomial and Negative Binomial Distributions for Dependent Bernoulli Variables

We study the distributions of the random variables S_n and V_r related to a sequence of dependent Bernoulli variables, where S_n denotes the number of successes in n trials and V_r the number of trials necessary to obtain r successes. The purpose of this article is twofold: (1) Generalizing some results on the “nature” of the binomial and negative binomial distributions we show that S_n and V_r can follow any prescribed discrete distribution. The corresponding joint distributions of the Bernoulli variables are characterized as the solutions of systems of linear equations. (2) We consider a specific type of dependence of the Bernoulli variables, where the probability of a success depends only on the number of previous successes. We develop some theory based on new closed-form representations for the probability mass functions of S_n and V_r which enable direct computations of the probabilities.     

Stochastic Comparisons and Dependence of Spacings from Two Samples of Exponential Random Variables

Let X ₁,X ₂,…,X _n be independent exponential random variables such that X _i has hazard rate λ for i = 1,…,p and X _j has hazard rate λ* for j = p + 1,…,n, where 1 ≤ p < n. Denote by D _i:n (λ, λ*) = X _i:n  ? X _i?1:n the ith spacing of the order statistics X _1:n  ≤ X _2:n  ≤ ··· ≤ X _n:n , i = 1,…,n, where X _0:n ≡ 0. It is shown that the spacings (D _1,n ,D _2,n ,…,D _n:n ) are MTP₂, strengthening one result of Khaledi and Kochar (2000), and that (D _1:n (λ₂, λ*),…,D _n:n (λ₂, λ*)) ≤ _lr (D _1:n (λ₁, λ*),…,D _n:n (λ₁, λ*)) for λ₁ ≤ λ* ≤ λ₂, where ≤ _lr denotes the multivariate likelihood ratio order. A counterexample is also given to show that this comparison result is in general not true for λ* < λ₁ < λ₂.     

A two-stage design for multivariate estimation of proportions

ABSTRACT

In this article, the problem of estimation of the several proportions of two inter-dependent sensitive characteristics prevailing in a given population is considered. A new two-stage randomized response model has been proposed by extending Lee et al.’s (2013 Lee, C., Sedory, S., Singh, S (2013). Estimation at least seven measures of qualitative variables from a single sample using randomized response technique. Stat. Probab. Lett. 83(1):399–409.[Crossref], [Web of Science ®] , [Google Scholar]) model. The expressions for biases, variances, and mean square errors of different estimators have been provided. The relative efficiency comparisons of the proposed estimators has been made, numerically by considering the different practicable choices of the design parameters. It was observed that the proposed extended version performs efficiently than simple and crossed models of Lee et al. (2013 Lee, C., Sedory, S., Singh, S (2013). Estimation at least seven measures of qualitative variables from a single sample using randomized response technique. Stat. Probab. Lett. 83(1):399–409.[Crossref], [Web of Science ®] , [Google Scholar]).     

Reliability modeling of systems with two dependent degrading components based on gamma processes

Abstract

Many engineering systems have multiple components with more than one degradation measure which is dependent on each other due to their complex failure mechanisms, which results in some insurmountable difficulties for reliability work in engineering. To overcome these difficulties, the system reliability prediction approaches based on performance degradation theory develop rapidly in recent years, and show their superiority over the traditional approaches in many applications. This paper proposes reliability models of systems with two dependent degrading components. It is assumed that the degradation paths of the components are governed by gamma processes. For a parallel system, its failure probability function can be approximated by the bivariate Birnbaum–Saunders distribution. According to the relationship of parallel and series systems, it is easy to find that the failure probability function of a series system can be expressed by the bivariate Birnbaum–Saunders distribution and its marginal distributions. The model in such a situation is very complicated and analytically intractable, and becomes cumbersome from a computational viewpoint. For this reason, the Bayesian Markov chain Monte Carlo method is developed for this problem that allows the maximum likelihood estimates of the parameters to be determined in an efficient manner. After that, the confidence intervals of the failure probability of systems are given. For an illustration of the proposed model, a numerical example about railway track is presented.     

The ruin probabilities of a discrete time risk model with one-sided linear claim sizes and dependent risks

This article investigates the ruin probabilities of a discrete time risk model with dependent claim sizes and dependent relation between insurance risks and financial risks. The risk-free and risky investments of an insurer lead to stochastic discount factors {θ_n}_{n ? 1}. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed (i.i.d.) innovations {?_n}_{n ? 1}. The i.i.d. random pairs {(?_n, θ_n)}_{n ? 1} follow a common bivariate Sarmanov-dependent distribution. When the common distribution of the innovations is heavy tailed, we establish some asymptotic estimates for the ruin probabilities of this discrete time risk model.     

Childhood Abuse and Welfare Use

Policies aimed at reducing welfare use focus solely on adults, yet welfare users very often report experiences of childhood abuse. Such abuse is known to have long-term psychological effects and may set the stage for later welfare use. This study uses a random sample of poor women to determine how a history of childhood abuse relates to the probability of receiving cash and in-kind assistance over a five-year period. It also investigate whether childhood abuse correlates with the length of receipt among program users. Women experiencing both physical and sexual abuse during childhood were 16–25 percentage points more likely than others to use both cash and in-kind programs as adults. Conditional on program use, there was no relation of childhood abuse to the extent of program use during the study period.     

Estimation of Survival Function Subject to Time-Dependent Covariates and Left Truncation

Abstract

Satten et al. [Satten, G. A., Datta, S., Robins, J. M. (2001). Estimating the marginal survival function in the presence of time dependent covariates. Statis. Prob. Lett. 54: 397--403] proposed an estimator [denoted by ?(t)] of survival function of failure times that is in the class of survival function estimators proposed by Robins [Robins, J. M. (1993). Information recovery and bias adjustment in proportional hazards regression analysis of randomized trials using surrogate markers. In: Proceedings of the American Statistical Association-Biopharmaceutical Section. Alexandria, VA: ASA, pp. 24--33]. The estimator is appropriate when data are subject to dependent censoring. In this article, it is demonstrated that the estimator ?(t) can be extended to estimate the survival function when data are subject to dependent censoring and left truncation. In addition, we propose an alternative estimator of survival function [denoted by ? _w (t)] that is represented as an inverse-probability-weighted average Satten and Datta [Satten, G. A., Datta, S. (2001). The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. Ass. 55: 207--210]. Simulation results show that when truncation is not severe the mean squared error of ?(t) is smaller than that of ? _w (t), except for the case when censoring is light. However, when truncation is severe, ? _w (t) has the advantage of less bias and the situation can be reversed.