Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of ...Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.展开更多
In standard interval mapping (IM) of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. When this assumption of normality is violated, the most commonly adopted strategy is to use th...In standard interval mapping (IM) of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. When this assumption of normality is violated, the most commonly adopted strategy is to use the previous model after data transformation. However, an appropriate transformation may not exist or may be difficult to find. Also this approach can raise interpretation issues. An interesting alternative is to consider a skew-normal mixture model in standard IM, and the resulting method is here denoted as skew-normal IM. This flexible model that includes the usual symmetric normal distribution as a special case is important, allowing continuous variation from normality to non-normality. In this paper we briefly introduce the main peculiarities of the skew-normal distribution. The maximum likelihood estimates of parameters of the skew-normal distribution are obtained by the expectation-maximization (EM) algorithm. The proposed model is illustrated with real data from an intercross experiment that shows a significant departure from the normality assumption. The performance of the skew-normal IM is assessed via stochastic simulation. The results indicate that the skew-normal IM has higher power for QTL detection and better precision of QTL location as compared to standard IM and nonparametric IM.展开更多
High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, vario...High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.展开更多
A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to d...A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to describe the distribution of responses in treated subjects for such studies. In this paper, we first study the mixture normal model with multi-levels and multiple mixture sub-populations under each level, with particular attention being given to the model in which the proportions of susceptibility are related to dose levels, then we use EM-algorithm to find the maximum likelihood estimators of model parameters. Our results are generalizations of the existing results. Finally, we illustrate realistic significance of the above extension based on a set of real dose-response data.展开更多
Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studie...Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mix<span>ture model. The mixing distribution is a finite mixture of two special cases of</span><span> Generalised Inverse Gaussian distribution with indexes <span style="white-space:nowrap;">-1/2 and -3/2</span>. The </span><span>parameters of the mixed model are obtained via the Expectation-Maximization</span><span> (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.展开更多
<p> <span style="color:#000000;"><span style="color:#000000;">Normal Variance-Mean Mixture (NVMM) provide</span></span><span style="color:#000000;"><...<p> <span style="color:#000000;"><span style="color:#000000;">Normal Variance-Mean Mixture (NVMM) provide</span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">s</span></span></span><span><span><span><span style="color:#000000;"> a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, </span><i><span style="color:#000000;">i.e.</span></i><span style="color:#000000;"> daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. </span><span style="color:#000000;">The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-</span><span style="color:#000000;">Nielsen </span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">(1977)</span></span></span><span><span><span><span style="color:#000000;"> which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, </span><i><span style="color:#000000;">i.e</span></i></span></span></span><span style="color:#000000;"><span style="color:#000000;"><i><span style="color:#000000;">.</span></i></span></span><span><span><span><span style="color:#000000;">, the index parameter of the GIG is</span><span style="color:red;"> <img src="Edit_721a4317-7ef5-4796-9713-b9057bc426fc.bmp" alt="" /></span><span style="color:#000000;">. The NIG is very popular because of its analytical tractability. In the mixing mechanism</span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">,</span></span></span><span><span><span><span><span style="color:#000000;"> the mixing distribution characterizes the prior informa展开更多
In this paper, the estimation of parameters based on a progressively typeI interval censored sample from a Pareto distribution is studied. Different methods of estimation are discussed, which include mid-point approxi...In this paper, the estimation of parameters based on a progressively typeI interval censored sample from a Pareto distribution is studied. Different methods of estimation are discussed, which include mid-point approximation estimator, the maximum likelihood estimator and moment estimator. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.展开更多
In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is considered.Our goal is to recover the corresponding quadratic objective function using noisy o...In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is considered.Our goal is to recover the corresponding quadratic objective function using noisy observations.First,the identifability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifable.Next,we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown,yet the exact observations on the initial states are available.We formulate the problem as a risk minimization problem and approximate the problem using empirical average.It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees.We then study the case where the exact observations on the initial states are not available,yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian(with unknown mean and covariance).EM-algorithm is used to estimate the parameters in the objective function.The efectiveness of our results are demonstrated by numerical examples.展开更多
文摘Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.
基金Project supported in part by Foundation for Science and Technology(FCT) (No.SFRD/BD/5987/2001)the Operational ProgramScience,Technology,and Innovation of the FCT,co-financed by theEuropean Regional Development Fund (ERDF)
文摘In standard interval mapping (IM) of quantitative trait loci (QTL), the QTL effect is described by a normal mixture model. When this assumption of normality is violated, the most commonly adopted strategy is to use the previous model after data transformation. However, an appropriate transformation may not exist or may be difficult to find. Also this approach can raise interpretation issues. An interesting alternative is to consider a skew-normal mixture model in standard IM, and the resulting method is here denoted as skew-normal IM. This flexible model that includes the usual symmetric normal distribution as a special case is important, allowing continuous variation from normality to non-normality. In this paper we briefly introduce the main peculiarities of the skew-normal distribution. The maximum likelihood estimates of parameters of the skew-normal distribution are obtained by the expectation-maximization (EM) algorithm. The proposed model is illustrated with real data from an intercross experiment that shows a significant departure from the normality assumption. The performance of the skew-normal IM is assessed via stochastic simulation. The results indicate that the skew-normal IM has higher power for QTL detection and better precision of QTL location as compared to standard IM and nonparametric IM.
文摘High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.
基金Supported by the National Natural Science Foundation of China (No. 10571073)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070183023)Program for New Century Excellent Talents in University, Scientific Research Fund of Jilin University (No. 200810024)
文摘A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to describe the distribution of responses in treated subjects for such studies. In this paper, we first study the mixture normal model with multi-levels and multiple mixture sub-populations under each level, with particular attention being given to the model in which the proportions of susceptibility are related to dose levels, then we use EM-algorithm to find the maximum likelihood estimators of model parameters. Our results are generalizations of the existing results. Finally, we illustrate realistic significance of the above extension based on a set of real dose-response data.
文摘Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mix<span>ture model. The mixing distribution is a finite mixture of two special cases of</span><span> Generalised Inverse Gaussian distribution with indexes <span style="white-space:nowrap;">-1/2 and -3/2</span>. The </span><span>parameters of the mixed model are obtained via the Expectation-Maximization</span><span> (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.
文摘<p> <span style="color:#000000;"><span style="color:#000000;">Normal Variance-Mean Mixture (NVMM) provide</span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">s</span></span></span><span><span><span><span style="color:#000000;"> a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, </span><i><span style="color:#000000;">i.e.</span></i><span style="color:#000000;"> daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. </span><span style="color:#000000;">The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-</span><span style="color:#000000;">Nielsen </span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">(1977)</span></span></span><span><span><span><span style="color:#000000;"> which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, </span><i><span style="color:#000000;">i.e</span></i></span></span></span><span style="color:#000000;"><span style="color:#000000;"><i><span style="color:#000000;">.</span></i></span></span><span><span><span><span style="color:#000000;">, the index parameter of the GIG is</span><span style="color:red;"> <img src="Edit_721a4317-7ef5-4796-9713-b9057bc426fc.bmp" alt="" /></span><span style="color:#000000;">. The NIG is very popular because of its analytical tractability. In the mixing mechanism</span></span></span></span><span style="color:#000000;"><span style="color:#000000;"><span style="color:#000000;">,</span></span></span><span><span><span><span><span style="color:#000000;"> the mixing distribution characterizes the prior informa
基金The NSF (11271155,11001105,11071126,10926156 and 11071269) of Chinathe Specialized Research Fund (20110061110003 and 20090061120037) for the Doctoral Program of Higher Education+1 种基金the General Humanities and Social Science Research Projects (11YJAZH125) Sponsored by Ministry of Educationthe Science and Technology Development Program (201201082) of Jilin Province
文摘In this paper, the estimation of parameters based on a progressively typeI interval censored sample from a Pareto distribution is studied. Different methods of estimation are discussed, which include mid-point approximation estimator, the maximum likelihood estimator and moment estimator. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.
文摘In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is considered.Our goal is to recover the corresponding quadratic objective function using noisy observations.First,the identifability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifable.Next,we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown,yet the exact observations on the initial states are available.We formulate the problem as a risk minimization problem and approximate the problem using empirical average.It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees.We then study the case where the exact observations on the initial states are not available,yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian(with unknown mean and covariance).EM-algorithm is used to estimate the parameters in the objective function.The efectiveness of our results are demonstrated by numerical examples.
