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The compound class of linear failure rate-power series distributions: Model, properties, and applications

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2017年第2期46卷 1414-1440页

作者： Mahmoudi, Eisa Jafari, A. A. Yazd Univ Dept Stat Pejoohesh St Safa Ieh 89195741 Yazd Iran

In this article, a new class of distributions is introduced, which generalizes the linear failure rate distribution and is obtained by compounding this distribution and power series class of distributions. This new class of distributions is called the linear failure rate-power series distributions and contains some new distributions such as linear failure rate-geometric, linear failure rate-Poisson, linear failure rate-logarithmic, linear failure rate-binomial distributions, and Rayleigh-power series class of distributions. Some former works such as exponential-power series class of distributions, exponential-geometric, exponential-Poisson, and exponential-logarithmic distributions are special cases of the new proposed model. The ability of the linear failure rate-power series class of distributions is in covering five possible hazard rate function, that is, increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of this class of distributions such as moments, maximum likelihood estimation procedure via an em-algorithm and inference for a large sample, are discussed in this article. In order to show the flexibility and potentiality, the fitted results of the new class of distributions and some of its submodels are compared using two real datasets.

关键词： em-algorithm Linear failure rate distribution Maximum likelihood estimation Moments Monte Carlo simulation Power series class of distributions

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An Akaike information criterion for multiple event mixture cure models

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期241卷 449-457页

作者： Dirick, Lore Claeskens, Gerda Baesens, Bart Katholieke Univ Leuven ORSTAT & Leuven Stat Res Ctr B-3000 Leuven Belgium Katholieke Univ Leuven LIRIS Fac Econ & Business B-3000 Leuven Belgium

We derive the proper form of the Akaike information criterion for variable selection for mixture cure models, which are often fit via the expectation-maximization algorithm. Separate covariate sets may be used in the mixture components. The selection criteria are applicable to survival models for right-censored data with multiple competing risks and allow for the presence of a non-susceptible group. The method is illustrated on credit loan data, with pre-payment and default as events and maturity as the non-susceptible case and is used in a simulation study. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Akaike information criterion Competing risks em-algorithm Mixture cure model Model selection

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COMFORT: A common market factor non-Gaussian returns model

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JOURNAL OF ECONOMETRICS 2015年第2期187卷 593-605页

作者： Paolella, Marc S. Polak, Pawel Univ Zurich Dept Banking & Finance CH-8006 Zurich Switzerland Columbia Univ Dept Stat New York NY 10027 USA Swiss Finance Inst Zurich Switzerland

A new multivariate time series model with various attractive properties is motivated and studied. By extending the CCC model in several ways, it allows for all the primary stylized facts of financial asset returns, including volatility clustering, non-normality (excess kurtosis and asymmetry), and also dynamics in the dependency between assets over time. A fast em-algorithm is developed for estimation. Each element of the vector return at time t is endowed with a common univariate shock, interpretable as a common market factor. This leads to the new model being a hybrid of GARCH and stochastic volatility, but without the estimation problems associated with the latter, and being applicable in the multivariate setting for potentially large numbers of assets. A feasible technique which allows for multivariate option pricing is presented, along with an empirical illustration. (C) 2015 Elsevier B.V. All rights reserved.

关键词： CCC Common jumps Density forecasting em-algorithm Fat tails GARCH Multivariate asymmetric variance gamma distribution Multivariate generalized hyperbolic distribution Multivariate option pricing Stochastic volatility

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Adjustment for misclassification in studies of familial aggregation of disease using routine register data

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STATISTICS IN MEDICINE 2002年第23期21卷 3595-3607页

作者： Andersen, EW Andersen, PK Danish Epidemiol Sci Ctr Statens Serum Inst DK-2300 Copenhagen S Denmark Univ Copenhagen Dept Biostat DK-2200 Copenhagen Denmark

This paper discusses the misclassification that occurs when relying solely on routine register data in family studies of disease clustering. A register study of familial aggregation of schizophrenia is used as an example. The familial aggregation is studied using a regression model for the disease in the child including the disease status of the parents as a risk factor. If all the information is found in the routine registers then the disease status of the parents is only known from the time when the register started and if this information is used unquestioningly the parents who have had the disease before this time are misclassified as disease-free. Two methods are presented to adjust for this misclassification: regression calibration and an em-type algorithm. These methods are used in the schizophrenia example where the large effect of having a schizophrenic mother hardly shows any signs of bias due to misclassification. The methods are also studied in simulations showing that the misclassification problem increases with the disease frequency. Copyright (C) 2002 John Wiley Sons, Ltd.

关键词： disease register em-algorithm familial aggregation misclassification nested case-control study regression calibration

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Prediction of future censored lifetimes from mixture exponential distribution

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METRIKA 2022年第7期85卷 833-857页

作者： Bdair, Omar M. Raqab, Mohammad Z. Al Balqa Appl Univ Fac Engn Technol Amman 11134 Jordan McMaster Univ Dept Math & Stat Hamilton ON L8S 4L8 Canada Univ Jordan Fac Sci Dept Math Amman 11942 Jordan

On the basis of a Type-II censored sample, Barakat et al. (Predicting future lifetimes of mixture exponential distribution, Commun Stat Simul Comput https://***/10.1080/03610918.2020.1715434, 2020) considered the problem of predicting the unobserved censored units from a mixture exponential distribution with known parameters. They then discussed how to use the pivotal quantity for obtaining prediction intervals for non-random and random sample size when all parameters are known. In this work, we consider the same problem of prediction where the model parameters involving the scale parameters as well as the mixing proportion parameter are all unknown. Further, we propose different prediction methods for obtaining prediction intervals of future lifetimes including likelihood, highest conditional median, and parametric bootstrap methods. In this set-up, two cases are considered. In the first case, we assume that the sample size is non-random, while in the second case, the sample size is assumed to be random number. It is shown from our numerical results that the parametric bootstrap-based prediction intervals are comparable in terms of coverage probability and very competitive in terms of average length when compared to all other prediction intervals considered in this paper.

关键词： em-algorithm Maximum likelihood estimation Mixed exponential distribution Monte Carlo simulation Prediction interval Type-II censoring

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Estimation and diagnostic analysis in skew-generalized-normal regression models

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2018年第6期88卷 1039-1059页

作者： Ferreira, Clecio S. Arellano-Valle, Reinaldo B. Univ Fed Juiz de Fora Dept Estat BR-36036900 Juiz De Fora MG Brazil Pontificia Univ Catolica Chile Dept Estadist Santiago Chile

The skew-generalized-normal distribution [Arellano-Valle, RB, Gomez, HW, Quintana, FA. A new class of skew-normal distributions. Comm Statist Theory Methods 2004;33(7):1465-1480] is a class of asymmetric normal distributions, which contains the normal and skew-normal distributions as special cases. The main virtues of this distribution is that it is easy to simulate from and it also supplies a genuine expectation-maximization (em) algorithm for maximum likelihood estimation. In this paper, we extend the em algorithm for linear regression models assuming skew-generalized-normal random errors and we develop a diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach would be more complicated to use to obtain measures of local influence. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.

关键词： Shape parameter skewness leverage local influence em-algorithm

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A METHOD FOR ESTIMATING THE AGE-SPECIFIC RELATIVE RISK OF HIV-INFECTION FROM AIDS INCIDENCE DATA

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BIOMETRIKA 1993年第1期80卷 165-178页

作者： BECKER, NG MARSCHNER, IC Department of Statistics La Trobe University Bundoora Victoria Australia 3083

Using a multiplicative model, the age-specific relative risk of infection with the human immunodeficiency virus, HIV, and the time-dependent HIV infection rate can be estimated simultaneously from acquired immunodeficiency syndrome, AIDS, incidence data. Non-parametric estimates are arrived at by an em-algorithm, with smoothing, applied to a back-projection model. The method gives estimates which lie on a smooth curve in accordance with strong prior expectations. The approach is illustrated with an application to Australian AIDS data. It is found that the HIV infection rate tends to be estimated more precisely when age is included as a covariate.

关键词： AIDS COUNTS BACK-PROJECTION BOOTSTRAP em-algorithm HUMAN IMMUNODEFICIENCY VIRUS INFECTION RATE NONPARAMETRIC ESTIMATION RELATIVE RISK SMOOTHING

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A folded model for compositional data analysis

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AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 2020年第2期62卷 249-277页

作者： Tsagris, Michail Stewart, Connie Univ Crete Dept Econom Rethimnon Greece Univ New Brunswick Dept Math & Stat St John NB Canada

A folded type model is developed for analysing compositional data. The proposed model involves an extension of the alpha-transformation for compositional data and provides a new and flexible class of distributions for modelling data defined on the simplex sample space. Despite its rather seemingly complex structure, employment of the em algorithm guarantees efficient parameter estimation. The model is validated through simulation studies and examples which illustrate that the proposed model performs better in terms of capturing the data structure, when compared to the popular logistic normal distribution, and can be advantageous over a similar model without folding.

关键词： alpha-transformation em-algorithm compositional data folding transformation

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Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2011年第1期141卷 462-473页

作者： Coretto, Pietro Hennig, Christian Univ Salerno Dept Econ & Stat Salerno Italy UCL Dept Stat Sci London WC1E 6BT England

Existence and consistency of the Maximum Likelihood estimator of the parameters of heterogeneous mixtures of Gaussian and uniform distributions with known number of components are shown under constraints to prevent the likelihood from degeneration and to ensure identifiability. The em-algorithm is discussed, and for the special case with a single uniform component a practical scheme to find a good local optimum is proposed. The method is compared theoretically and empirically to the estimation of a Gaussian mixture with "noise component" as introduced by Banfield and Raftery (1993) to find out whether it is a worthwhile alternative particularly in situations with outliers and points not belonging to the Gaussian components. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Model-based clustering Robustness Identifiability em-algorithm Hathaway constraints Noise component

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Exponential-modified discrete Lindley distribution

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SPRINGERPLUS 2016年第1期5卷 1660页

作者： Yilmaz, Mehmet Hameldarbandi, Monireh Kemaloglu, Sibel Acik Ankara Univ Dept Stat Fac Sci TR-06100 Ankara Turkey Ankara Univ Grad Sch Nat & Appl Sci TR-06110 Ankara Turkey

In this study, we have considered a series system composed of stochastically independent M-component where M is a random variable having the zero truncated modified discrete Lindley distribution. This distribution is newly introduced by transforming on original parameter. The properties of the distribution of the lifetime of above system have been examined under the given circumstances and also parameters of this new lifetime distribution are estimated by using moments, maximum likelihood and em-algorithm.

关键词： Modified discrete Lindley distribution Exponential-modified Discrete Lindley distribution Method of moments Maximum likelihood estimation em-algorithm

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