In this paper, the author considers a new Loss-distribution-approach model, in which the over-dispersed operational risks are modeled by the compound negative binomial process. In the single dimensional case, asymptot...In this paper, the author considers a new Loss-distribution-approach model, in which the over-dispersed operational risks are modeled by the compound negative binomial process. In the single dimensional case, asymptotic expansion for the quantile of compound negative binomial process is explored for computing the capital charge of a bank for operational risk. Moreover, when the dependence structure between different risk cells is modeled by the Frank copula, this approach is extended to the multi-dimensional setting. A practical example is given to demonstrate the effectiveness of approximation results.展开更多
For stochastic loss reserving,we propose an individual information model(IIM)which accom-modates not only individual/micro data consisting of incurring times,reporting developments,settlement developments as well as p...For stochastic loss reserving,we propose an individual information model(IIM)which accom-modates not only individual/micro data consisting of incurring times,reporting developments,settlement developments as well as payments of individual claims but also heterogeneity among policies.We give over-dispersed Poisson assumption about the moments of reporting developments and payments of every individual claims.Model estimation is conducted under quasi-likelihood theory.Analytic expressions are derived for the expectation and variance of outstanding liabilities,given historical observations.We utilise conditional mean square error of prediction(MSEP)to measure the accuracy of loss reserving and also theoretically prove that when risk portfolio size is large enough,IIM shows a higher prediction accuracy than individ-ual/micro data model(IDM)in predicting the outstanding liabilities,if the heterogeneity indeed influences claims developments and otherwise IIM is asymptotically equivalent to IDM.Some simulations are conducted to investigate the conditional MSEPs for IIM and IDM.A real data analysis is performed basing on real observations in health insurance.展开更多
Count data is almost always over-dispersed where the variance exceeds the mean. Several count data models have been proposed by researchers but the problem of over-dispersion still remains unresolved, more so in the c...Count data is almost always over-dispersed where the variance exceeds the mean. Several count data models have been proposed by researchers but the problem of over-dispersion still remains unresolved, more so in the context of change point analysis. This study develops a likelihood-based algorithm that detects and estimates multiple change points in a set of count data assumed to follow the Negative Binomial distribution. Discrete change point procedures discussed in literature work well for equi-dispersed data. The new algorithm produces reliable estimates of change points in cases of both equi-dispersed and over-dispersed count data;hence its advantage over other count data change point techniques. The Negative Binomial Multiple Change Point Algorithm was tested using simulated data for different sample sizes and varying positions of change. Changes in the distribution parameters were detected and estimated by conducting a likelihood ratio test on several partitions of data obtained through step-wise recursive binary segmentation. Critical values for the likelihood ratio test were developed and used to check for significance of the maximum likelihood estimates of the change points. The change point algorithm was found to work best for large datasets, though it also works well for small and medium-sized datasets with little to no error in the location of change points. The algorithm correctly detects changes when present and fails to detect changes when change is absent in actual sense. Power analysis of the likelihood ratio test for change was performed through Monte-Carlo simulation in the single change point setting. Sensitivity analysis of the test power showed that likelihood ratio test is the most powerful when the simulated change points are located mid-way through the sample data as opposed to when changes were located in the periphery. Further, the test is more powerful when the change was located three-quarter-way through the sample data compared to when the change point is closer (quarter-way) to the first observation.展开更多
Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We dis...Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.展开更多
Road traffic crash data are useful tools to support the development, implementation, and assessment of highway safety programs that tend to reduce road traffic crashes. Collecting road traffic crash data aims at gaini...Road traffic crash data are useful tools to support the development, implementation, and assessment of highway safety programs that tend to reduce road traffic crashes. Collecting road traffic crash data aims at gaining a better understanding of road traffic operational problems, locating hazardous road sections, identifying risk factors, developing accurate diagnosis and remedial measures, and evaluating the effectiveness of road safety programs. Furthermore, they can be used by many agencies and businesses such as: law enforcements to identify persons at fault in road traffic crashes;insurers seeking facts about traffic crash claims;road safety researchers to access traffic crash reliable database;decision makers to develop long-term, statewide strategic plans for traffic and highway safety;and highway safety administrators to help educate the public. Given the practical importance of vehicle crash data, this paper presents an overview of the sources, trends and problems associated with road traffic crash data.展开更多
Within the family of zero-inflated Poisson distributions, the data has Poisson distribution if any only if the mean equals the variance. In this paper we compare two closely related test statistics constructed based o...Within the family of zero-inflated Poisson distributions, the data has Poisson distribution if any only if the mean equals the variance. In this paper we compare two closely related test statistics constructed based on this idea. Our results show that although these two tests are asymptotically equivalent under the null hypothesis and are equally efficient, one test is always more efficient than the other one for small and medium sample sizes.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11201001 in partthe Science Research Grant of Shaanxi Province under Grant No.2011JM1019the Foundation Research Project of Engineering University of CAPF under Grant No.WJY201304
文摘In this paper, the author considers a new Loss-distribution-approach model, in which the over-dispersed operational risks are modeled by the compound negative binomial process. In the single dimensional case, asymptotic expansion for the quantile of compound negative binomial process is explored for computing the capital charge of a bank for operational risk. Moreover, when the dependence structure between different risk cells is modeled by the Frank copula, this approach is extended to the multi-dimensional setting. A practical example is given to demonstrate the effectiveness of approximation results.
基金This work was supported by the Natural Science Foundation of China(71771089)the Shanghai Philosophy and Social Sci-ence Foundation(2015BGL001)+1 种基金the National Social Science Foundation Key Program of China(17ZDA091)China Scholarship Council(201906140045)。
文摘For stochastic loss reserving,we propose an individual information model(IIM)which accom-modates not only individual/micro data consisting of incurring times,reporting developments,settlement developments as well as payments of individual claims but also heterogeneity among policies.We give over-dispersed Poisson assumption about the moments of reporting developments and payments of every individual claims.Model estimation is conducted under quasi-likelihood theory.Analytic expressions are derived for the expectation and variance of outstanding liabilities,given historical observations.We utilise conditional mean square error of prediction(MSEP)to measure the accuracy of loss reserving and also theoretically prove that when risk portfolio size is large enough,IIM shows a higher prediction accuracy than individ-ual/micro data model(IDM)in predicting the outstanding liabilities,if the heterogeneity indeed influences claims developments and otherwise IIM is asymptotically equivalent to IDM.Some simulations are conducted to investigate the conditional MSEPs for IIM and IDM.A real data analysis is performed basing on real observations in health insurance.
文摘Count data is almost always over-dispersed where the variance exceeds the mean. Several count data models have been proposed by researchers but the problem of over-dispersion still remains unresolved, more so in the context of change point analysis. This study develops a likelihood-based algorithm that detects and estimates multiple change points in a set of count data assumed to follow the Negative Binomial distribution. Discrete change point procedures discussed in literature work well for equi-dispersed data. The new algorithm produces reliable estimates of change points in cases of both equi-dispersed and over-dispersed count data;hence its advantage over other count data change point techniques. The Negative Binomial Multiple Change Point Algorithm was tested using simulated data for different sample sizes and varying positions of change. Changes in the distribution parameters were detected and estimated by conducting a likelihood ratio test on several partitions of data obtained through step-wise recursive binary segmentation. Critical values for the likelihood ratio test were developed and used to check for significance of the maximum likelihood estimates of the change points. The change point algorithm was found to work best for large datasets, though it also works well for small and medium-sized datasets with little to no error in the location of change points. The algorithm correctly detects changes when present and fails to detect changes when change is absent in actual sense. Power analysis of the likelihood ratio test for change was performed through Monte-Carlo simulation in the single change point setting. Sensitivity analysis of the test power showed that likelihood ratio test is the most powerful when the simulated change points are located mid-way through the sample data as opposed to when changes were located in the periphery. Further, the test is more powerful when the change was located three-quarter-way through the sample data compared to when the change point is closer (quarter-way) to the first observation.
文摘Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.
文摘Road traffic crash data are useful tools to support the development, implementation, and assessment of highway safety programs that tend to reduce road traffic crashes. Collecting road traffic crash data aims at gaining a better understanding of road traffic operational problems, locating hazardous road sections, identifying risk factors, developing accurate diagnosis and remedial measures, and evaluating the effectiveness of road safety programs. Furthermore, they can be used by many agencies and businesses such as: law enforcements to identify persons at fault in road traffic crashes;insurers seeking facts about traffic crash claims;road safety researchers to access traffic crash reliable database;decision makers to develop long-term, statewide strategic plans for traffic and highway safety;and highway safety administrators to help educate the public. Given the practical importance of vehicle crash data, this paper presents an overview of the sources, trends and problems associated with road traffic crash data.
文摘Within the family of zero-inflated Poisson distributions, the data has Poisson distribution if any only if the mean equals the variance. In this paper we compare two closely related test statistics constructed based on this idea. Our results show that although these two tests are asymptotically equivalent under the null hypothesis and are equally efficient, one test is always more efficient than the other one for small and medium sample sizes.
