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A uniform-Laplace mixture distribution

JOURNAL OF COMPUTATIONAL AND APPLIED MATHemATICS 2023年第1期429卷

作者： Natido, Amos Kozubowski, Tomasz J. Univ Nevada Dept Math & Stat Reno NV 89557 USA

We introduce a new stochastic model incorporating a mixture of uniform and Laplace distributions. We present basic theoretical properties of this model and discuss related computational issues of parameter estimation via expectation-maximization computa-tional schemes. We check the performance of the estimation algorithm on synthetic data and provide a data example illustrating modeling potential of this novel methodology. A related model involving a mixture of uniform and exponential distributions is studied as well along the same lines.(c) 2023 Elsevier B.V. All rights reserved.

关键词： em-algorithm Finite mixture model Gaussian-uniform mixture Laplace distribution Maximum likelihood estimation Renewable energy

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A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data

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Applied Mathematics 2022年第2期13卷 163-177页

作者： Calvin B. Maina Patrick G. O. Weke Carolyne A. Ogutu Joseph A. M. Ottieno Department of Mathematics and Actuarial Science Kisii University Kisii Kenya School of Mathematics University of Nairobi Nairobi Kenya

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.

关键词： Inverse Gaussian Finite Mixture Weighted Distribution Mixed Model em-algorithm

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A Special Weight for Inverse Gaussian Mixing Distribution in Normal Variance Mean Mixture with Application

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Open Journal of Statistics 2021年第6期11卷 977-992页

Normal Variance-Mean Mixture (NVMM) provides 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, i.e. daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-Nielsen (1977) 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, i.e., the index parameter of the GIG is . The NIG is very popular because of its analytical tractability. In the mixing mechanism, the mix

关键词： Finite Mixture Weighted Distribution Mixed Model em-algorithm

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Modelling Skewed And Heavy-tailed Data Using A Normal Weighted Inverse Gaussian Distribution

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Afrika Statistika 2022年第1期17卷 3165-3187页

作者： Calvin Maina Patrick Guge Weke Carolyne Adhiambo Ogutu Joseph Makoteku Ottieno

The normal distribution is inadequate in capturing skewed and heavy-tailed behaviour of data taken over short time intervals. In addition the data can be leptokurtic. For this reason a normal weighted inverse Gaussian distribution is proposed as an alternative to the normal inverse Gaussian distribution to handle such data. The mixing distribution used in the normal variance mean mixture is a finite mixture of two special cases of Generalized Inverse Gaussian ( GIG ) distribution. The two special cases and the finite mixture are weighted inverse Gaussian distribution. The motivation for this work is that a finite mixture is more flexible than a single/standard distribution. The em -algorithm has been used for parameter estimation. Pour traiter des données présentant une asymétrie, une queue lourde et un caractère leptokurtique, nous proposons un modèle de mélange en variance où la variable de mélange est elle-même un mélange pondéré de deux loi normales inverses. L'algorithme em est utilisé pour l'estimation. Le modèle a été étudié et simulé avec succès.

关键词： 62P05 em-algorithm finite mixture mixing distribution NWIG

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Subspace identification of state space models with observation outliers based on least-trimmed-squares

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IFAC Proceedings Volumes 2004年第12期37卷 865-870页

作者： Jaafar Al Mutawa Tohru Katayama Department of Applied Mathematics and Physics Graduate School of Informatics Kyoto University Kyoto 606-8501 Japan

In this paper, we develop a subspace system identification method for linear stochastic systems subject to observation noise with outliers. By using the least-trimmed-squares (LTS), we identify the outliers and substitute the median of the output data for them, and then we apply the orthogonal decomposition (ORT) based method (Picci and Katayama, 1996 a ; Picci and Katayama, 1996 b ) to get state space models. A numerical example demonstrates the effectiveness of the proposed method. Also it is shown by numerical simulation that the model estimated by the ORT coupled with LTS can be further improved by the em-algorithm (Shumway and Stoffer, 1982; ALMutawa et al. , 2003) with considerable numerical effort.

关键词： Subspace system identification ORT Lest-trimmed-squares utliers em-algorithm

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A New Areal Interpolation Method Based on Spatial Statistics

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Procedia - Social and Behavioral Sciences 2011年 21卷 230-239页

作者： Daisuke Murakami Morito Tsutsumi Graduate School of Systems and Information Engineering University of Tsukuba 1-1-1 Tennodai Tsukuba Japan

Differences in spatial units among spatial data often complicate analyses. Spatial unit convergence, called areal interpolation, is often applied to address this problem. Of the many proposed areal interpolation methods, few consider spatial autocorrelation, which is the general property of spatial data. In this paper, by employing a spatial process model, a new areal interpolation method that considers spatial autocorrelation is presented. First, we briefly survey previous areal interpolation techniques and demonstrate that the stochastic method is superior to the deterministic method in archiving accurate interpolations. Next, after a discussion on the spatial process model, a new areal interpolation method is suggested. In this method, both spatial autocorrelation and the volume preserving property, a property that should be considered in areal interpolation, are considered using a combination of a linear regression based areal interpolation method, and the spatial process model. Finally, a case study on the areal interpolation of a population is provided to demonstrate that the suggested method succeeds in improving the predictive accuracy. This case study indicates that the consideration of spatial autocorrelation is important for accurate areal interpolation.

关键词： Areal interpolation Spatial dependence Spatial statistics em-algorithm Pycnophylactic property

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A Finite Mixture of Generalised Inverse Gaussian with Indexes -1/2 and -3/2 as Mixing Distribution for Normal Variance Mean Mixture with Application

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Open Journal of Statistics 2021年第6期11卷 963-976页

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 mixture model. The mixing distribution is a finite mixture of two special cases of Generalised Inverse Gaussian distribution with indexes -1/2 and -3/2. The parameters of the mixed model are obtained via the Expectation-Maximization (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.

关键词： Finite Mixture Weighted Distribution Mixed Model em-algorithm

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Maximum Likelihood Estimation of the Parameters of Exponentiated Generalized Weibull Based on Progressive Type II Censored Data

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Open Journal of Statistics 2017年第6期7卷 956-963页

作者： Ibrahim Sawadogo Leo Odongo Ibrahim Ly Pan African University Institute of Science Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Science Kenyatta University (KU) Nairobi Kenya Department of Mathematics University of Ouagadougou Ouagadougou Burkina Faso Department of Mathematics University of Potsdam Potsdam Germany

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.

关键词： Maximum Likelihood Type II Censored Data Exponentiated Generalized Weibull em-algorithm

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The analysis of incomplete cost data due to dropout

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HEALTH ECONOMICS 2005年第8期14卷 763-776页

作者： Oostenbrink, JB Al, MJ Erasmus MC Inst Med Technol Assessment NL-3000 DR Rotterdam Netherlands

Incomplete data due to premature withdrawal (dropout) constitute a serious problem in prospective economic evaluations that has received only little attention to date. The aim of this simulation study was to investigate how standard methods for dealing with incomplete data perform when applied to cost data with various distributions and various types of dropout. Selected methods included the product-limit estimator of Lin et al. the expectation maximisation (em-) algorithm, several types of multiple imputation (MI) and various simple methods like complete case analysis and mean imputation. Almost all methods were unbiased in the case of dropout completely at random (DCAR), but only the product-limit estimator, the em-algorithm and the MI approaches provided adequate estimates of the standard error (SE). The best estimates of the mean and SE for dropout at random (DAR) were provided by the bootstrap em-algorithm, MI regression and MI Monte Carlo Markov chain. These methods were able to deal with skewed cost data in combination with DAR and only became biased when costs also included the costs of expensive events. None of the methods were able to deal adequately with informative dropout. In conclusion, the em-algorithm with bootstrap, MI regression and MI MCMC are robust to the multivariate normal assumption and are the preferred methods for the analysis of incomplete cost data when the assumption of DCAR is not justified. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： dropout missing data censoring economic evaluation cost analysis multiple imputation em-algorithm

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Convergence of the algorithm of Additive Regularization of Topic Models

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PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHemATICS 2021年第SUPPL 1期315卷 S128-S139页

作者： Irkhin, I. A. Vorontsov, K. V. Natl Res Univ Moscow Inst Phys & Technol Dolgoprudnyi 141701 Russia

The problem of probabilistic topic modeling is as follows. Given a collection of text documents, find the conditional distribution over topics for each document and the conditional distribution over words (or terms) for each topic. Log-likelihood maximization is used to solve this problem. The problem generally has an infinite set of solutions and is ill-posed according to Hadamard. In the framework of Additive Regularization of Topic Models (ARTM), a weighted sum of regularization criteria is added to the main log-likelihood criterion. The numerical method for solving this optimization problem is a kind of an iterative em-algorithm written in a general form for an arbitrary smooth regularizer as well as for a linear combination of smooth regularizers. This paper studies the problem of convergence of the em iterative process. Sufficient conditions are obtained for the convergence to a stationary point of the regularized log-likelihood. The constraints imposed on the regularizer are not too restrictive. We give their interpretations from the point of view of the practical implementation of the algorithm. A modification of the algorithm is proposed that improves the convergence without additional time and memory costs. Experiments on a news text collection have shown that our modification both accelerates the convergence and improves the value of the criterion to be optimized.

关键词： natural language processing probabilistic topic modeling probabilistic latent semantic analysis (PLSA) latent Dirichlet allocation (LDA) additive regularization of topic models (ARTM) em-algorithm sufficient conditions for convergence

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