This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estima...This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.展开更多
Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In mos...Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.展开更多
In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an emp...In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared.展开更多
In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose ...In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.展开更多
This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theor...This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained. As a result, we obtain some strong deviation theorems for Poisson distribution and binomial distribution.展开更多
In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and sta...In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.展开更多
广义帕累托分布(GPD)在极值统计的POT模型中常常被用来逼近超过阈值u的超出量X_i-u的分布.为解决经典估计方法存在的问题,Zhang(Zhang J,Likelihood moment estimation for the generalized Pareto distribution,Aust N Z J Stat,2007,4...广义帕累托分布(GPD)在极值统计的POT模型中常常被用来逼近超过阈值u的超出量X_i-u的分布.为解决经典估计方法存在的问题,Zhang(Zhang J,Likelihood moment estimation for the generalized Pareto distribution,Aust N Z J Stat,2007,49:69-77)对两参数GPD(GP2)提出一种新的估计方法——似然矩估计(LM),它容易计算且具有较高的渐近有效性.本文将此方法从两参数的情形推广到三参数GPD(GP3),结果表明尺度参数和形状参数估计的渐近性质与以上所提到的文章完全相同.针对GP3的LM估计也具有总是存在、易于计算以及对绝大多数的形状参数具有接近于最小的偏差和均方误差的特点.展开更多
文摘This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.
文摘Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.
文摘In this article we study the empirical likelihood inference for AR（p） model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parametric, and we also propose an empirical log-likelihood ratio base on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotically standard chi-squared.
文摘In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.
文摘This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained. As a result, we obtain some strong deviation theorems for Poisson distribution and binomial distribution.
文摘In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.
文摘广义帕累托分布(GPD)在极值统计的POT模型中常常被用来逼近超过阈值u的超出量X_i-u的分布.为解决经典估计方法存在的问题,Zhang(Zhang J,Likelihood moment estimation for the generalized Pareto distribution,Aust N Z J Stat,2007,49:69-77)对两参数GPD(GP2)提出一种新的估计方法——似然矩估计(LM),它容易计算且具有较高的渐近有效性.本文将此方法从两参数的情形推广到三参数GPD(GP3),结果表明尺度参数和形状参数估计的渐近性质与以上所提到的文章完全相同.针对GP3的LM估计也具有总是存在、易于计算以及对绝大多数的形状参数具有接近于最小的偏差和均方误差的特点.
