Generalized method of moments based on probability generating function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square tests. The estimation...Generalized method of moments based on probability generating function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square tests. The estimation methods developed are also related to estimation methods based on generalized estimating equations but with the advantage of having statistics for model testing. The methods proposed overcome numerical problems often encountered when the probability mass functions have no closed forms which prevent the use of maximum likelihood (ML) procedures and in general, ML procedures do not lead to distribution free model testing statistics.展开更多
This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distribut...This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.展开更多
In this paper, we introduce a modification of the Quasi Lindley distribution which has various advantageous properties for the lifetime data. Several fundamental structural properties of the distribution are explored....In this paper, we introduce a modification of the Quasi Lindley distribution which has various advantageous properties for the lifetime data. Several fundamental structural properties of the distribution are explored. Its density function can be left-skewed, symmetrical, and right-skewed shapes with various rages of tail-weights and dispersions. The failure rate function of the new dist</span><span style="font-family:Verdana;">ribution has the flexibility to be increasing, decreasing, constant, an</span><span style="font-family:Verdana;">d bathtub shapes. A simulation study is done to examine the performance of maximum likelihood and moment estimation methods in its unknown parameter estimations based on the asymptotic theory. The potentiality of the new distribution is illustrated by means of applications to the simulated and three real-world data sets.展开更多
该文提出了一种基于遗传算法(genetic algorithm,GA)的有限混合分布参数估计方法,应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先,采用小波变换消除原始应变监测数据中的温度影响,利用雨流计数法将应变时程曲线转化为...该文提出了一种基于遗传算法(genetic algorithm,GA)的有限混合分布参数估计方法,应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先,采用小波变换消除原始应变监测数据中的温度影响,利用雨流计数法将应变时程曲线转化为日应力谱,考虑到交通荷载(包括汽车荷载和火车荷载)和台风的影响,建立标准日应力谱。然后,采用三种不同的有限混合分布函数(有限混合正态分布函数、有限混合对数正态分布函数和有限混合威布尔分布函数)以及基于遗传算法的混合参数估计方法对应力幅进行多模态建模,根据赤池信息准则(Akaike’s information criterion,AIC)确定最佳的有限混合模型。最后,采用双变量有限混合分布和基于遗传算法的混合参数估计方法建立了应力幅和平均应力二维随机变量联合概率密度函数。结果表明,该文提出的基于遗传算法的有限混合分布参数估计方法可以有效应用于二维随机变量的概率建模。展开更多
In this paper, we consider simulated minimum Hellinger distance (SMHD) inferences for count data. We consider grouped and ungrouped data and emphasize SMHD methods. The approaches extend the methods based on the deter...In this paper, we consider simulated minimum Hellinger distance (SMHD) inferences for count data. We consider grouped and ungrouped data and emphasize SMHD methods. The approaches extend the methods based on the deterministic version of Hellinger distance for count data. The methods are general, it only requires that random samples from the discrete parametric family can be drawn and can be used as alternative methods to estimation using probability generating function (pgf) or methods based matching moments. Whereas this paper focuses on count data, goodness of fit tests based on simulated Hellinger distance can also be applied for testing goodness of fit for continuous distributions when continuous observations are grouped into intervals like in the case of the traditional Pearson’s statistics. Asymptotic properties of the SMHD methods are studied and the methods appear to preserve the properties of having good efficiency and robustness of the deterministic version.展开更多
In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when ...In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.展开更多
文摘Generalized method of moments based on probability generating function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square tests. The estimation methods developed are also related to estimation methods based on generalized estimating equations but with the advantage of having statistics for model testing. The methods proposed overcome numerical problems often encountered when the probability mass functions have no closed forms which prevent the use of maximum likelihood (ML) procedures and in general, ML procedures do not lead to distribution free model testing statistics.
文摘This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.
文摘In this paper, we introduce a modification of the Quasi Lindley distribution which has various advantageous properties for the lifetime data. Several fundamental structural properties of the distribution are explored. Its density function can be left-skewed, symmetrical, and right-skewed shapes with various rages of tail-weights and dispersions. The failure rate function of the new dist</span><span style="font-family:Verdana;">ribution has the flexibility to be increasing, decreasing, constant, an</span><span style="font-family:Verdana;">d bathtub shapes. A simulation study is done to examine the performance of maximum likelihood and moment estimation methods in its unknown parameter estimations based on the asymptotic theory. The potentiality of the new distribution is illustrated by means of applications to the simulated and three real-world data sets.
文摘该文提出了一种基于遗传算法(genetic algorithm,GA)的有限混合分布参数估计方法,应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先,采用小波变换消除原始应变监测数据中的温度影响,利用雨流计数法将应变时程曲线转化为日应力谱,考虑到交通荷载(包括汽车荷载和火车荷载)和台风的影响,建立标准日应力谱。然后,采用三种不同的有限混合分布函数(有限混合正态分布函数、有限混合对数正态分布函数和有限混合威布尔分布函数)以及基于遗传算法的混合参数估计方法对应力幅进行多模态建模,根据赤池信息准则(Akaike’s information criterion,AIC)确定最佳的有限混合模型。最后,采用双变量有限混合分布和基于遗传算法的混合参数估计方法建立了应力幅和平均应力二维随机变量联合概率密度函数。结果表明,该文提出的基于遗传算法的有限混合分布参数估计方法可以有效应用于二维随机变量的概率建模。
文摘In this paper, we consider simulated minimum Hellinger distance (SMHD) inferences for count data. We consider grouped and ungrouped data and emphasize SMHD methods. The approaches extend the methods based on the deterministic version of Hellinger distance for count data. The methods are general, it only requires that random samples from the discrete parametric family can be drawn and can be used as alternative methods to estimation using probability generating function (pgf) or methods based matching moments. Whereas this paper focuses on count data, goodness of fit tests based on simulated Hellinger distance can also be applied for testing goodness of fit for continuous distributions when continuous observations are grouped into intervals like in the case of the traditional Pearson’s statistics. Asymptotic properties of the SMHD methods are studied and the methods appear to preserve the properties of having good efficiency and robustness of the deterministic version.
文摘In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.
