This article investigates autoregressive processes with the flexible and attractive symmetric/asymmetric and light/heavy tailed Generalized-Hyperbolic innovations. The Generalized-Hyperbolic family of distributions ha...
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This article investigates autoregressive processes with the flexible and attractive symmetric/asymmetric and light/heavy tailed Generalized-Hyperbolic innovations. The Generalized-Hyperbolic family of distributions has an interesting stochastic representation which can be used in simulating the proposed autoregressive model and estimating its parameters via an Expectation-Maximization (em) type algorithm. The performance of the proposed model and its estimation through a simulation study is also evaluated. The model is then applied on two real-time series datasets.
Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete a...
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Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete and incomplete information under continuous monitoring of the essential component lifetimes. First, we prove that the maximum likelihood estimator (MLE) under complete information based on progressively Type-II censored system lifetimes uniquely exists and we present two approaches to compute the estimates. Furthermore, we consider an ad hoc estimator, a max-probability plan estimator and the MLE for the parameters under incomplete information. In order to compute the MLEs, we consider a direct maximization of the likelihood and an em-algorithm-type approach, respectively. In all cases, we illustrate the results by simulations of the five-component bridge system and the 10-component parallel system, respectively.
This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose-response studies where the spontaneous or natural response rate is nonneglig...
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This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose-response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an emalgorithm for fitting the models. The emalgorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.
In this paper, we introduce a bivariate distribution on R(+)xN arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which a...
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In this paper, we introduce a bivariate distribution on R(+)xN arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which allow for flexible behavior for modeling purposes. We show that the distribution is dense in the class of distributions on R(+)xN and derive some of its main properties, all explicit in terms of matrix calculus. Furthermore, we develop an effective emalgorithm for the statistical estimation of the distribution parameters. In the last part of the paper, we apply our methodology to an insurance dataset, where we model the number of claims and the mean claim sizes of policyholders, which is seen to perform favorably. An additional consequence of the latter analysis is that the total loss size in the entire portfolio is captured substantially better than with independent phase-type models.
Although the hidden Markov models (HMM) are very popular in many applied areas their use in reliabil-ity engineering is limited. Problems such as the selection of the HMM model by choosing the appropriate number of st...
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Although the hidden Markov models (HMM) are very popular in many applied areas their use in reliabil-ity engineering is limited. Problems such as the selection of the HMM model by choosing the appropriate number of states, or problems of prediction of failures have not been widely covered in the literature. This paper is concerned with the use of HMMs where the state of the system is not directly observable and instead certain indicators of the true situation are provided via a control system. A hidden model can provide key information about the system dependability such as the failed component of the sys-tem, the reliability of the system and related measures. A maximum-likelihood estimator of the system reliability is obtained and its asymptotic properties are studied. Finally, the maintenance of the system is considered in this context and new preventive maintenance strategies are defined and their efficiency is measured in terms of expected cost. To prove the finite sample performance of the methodology, an extensive simulation study is developed.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )
In this article, an alternative estimation approach is proposed to fit linear mixed effects models where the random effects follow a finite mixture of normal distributions. This heterogeneity linear mixed model is an ...
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In this article, an alternative estimation approach is proposed to fit linear mixed effects models where the random effects follow a finite mixture of normal distributions. This heterogeneity linear mixed model is an interesting tool since it relaxes the classical normality assumption and is also perfectly suitable for classification purposes, based on longitudinal profiles. Instead of fitting directly the heterogeneity linear mixed model, we propose to fit an equivalent mixture of linear mixed models under some restrictions which is computationally simpler. Unlike the former model, the latter can be maximized analytically using an em-algorithm and the obtained parameter estimates can be easily used to compute the parameter estimates of interest.
The first model-based clustering algorithm for multivariate functional data is proposed. After introducing multivariate functional principal components analysis (MFPCA), a parametric mixture model, based on the assump...
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The first model-based clustering algorithm for multivariate functional data is proposed. After introducing multivariate functional principal components analysis (MFPCA), a parametric mixture model, based on the assumption of normality of the principal component scores, is defined and estimated by an em-like algorithm. The main advantage of the proposed model is its ability to take into account the dependence among curves. Results on simulated and real datasets show the efficiency of the proposed method. (C) 2012 Elsevier B.V. All rights reserved.
In practice, multivariate skew normal mixture (MSNM) models provide a more flexible framework than multivariate normal mixture models, especially for heterogeneous and asymmetric data. For MSNM models, the maximum lik...
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In practice, multivariate skew normal mixture (MSNM) models provide a more flexible framework than multivariate normal mixture models, especially for heterogeneous and asymmetric data. For MSNM models, the maximum likelihood estimator often leads to a statistical inference referred to as "badness" under certain properties, because of the unboundedness of the likelihood function and the divergence of shape parameters. We consider two penalties for the log-likelihood function to counter these issues simultaneously in MSNM models. We show that the penalized maximum likelihood estimator is strongly consistent when the putative order of the mixture is equal to or larger than the true order. We also provide penalized expectation-maximization-type algorithms to compute penalized estimates. Finite sample performance is examined through simulations, real data applications, and comparison with existing methods.
One-shot devices are products or equipments that can be used only once. A nature characteristic of one-shot devices is that they get destroyed immediately after their use, and therefore their actual lifetimes are neve...
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One-shot devices are products or equipments that can be used only once. A nature characteristic of one-shot devices is that they get destroyed immediately after their use, and therefore their actual lifetimes are never observable. The only information observed is the condition whether they worked or not at the time they are used. These days the quality of products are significantly improved, so that the information obtained under a normal test during a short time is quite limited. A typical test to induce more failures is the accelerated life-test, which is developed by increasing the stress levels under test. In this paper, we will investigate the reliability of one-shot devices with generalized gamma fatigue life under accelerated life-tests with various cyclic temperature fluctuations by assuming a Norris-Landzberg model. Generalized gamma involves many common lifetime distributions, such as gamma, Weibull, lognormal, and positive stable distributions, as special cases. Norris-Landzberg model takes not only temperature change, highest testing temperature, but also the cycling frequency into account when modeling the number of cycles-to-failure, resulting a generalized model with the well-known Coffin-Manson model and Coffin-Manson-Arrhenius model as special cases. Associated inferences are developed. The performance of the proposed model and inferential methods will be evaluated with simulation study and model discrimination. Finally, the chip-scale package solder joints data is analyzed to illustrate the considered model and inferential methods developed in this paper.
In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is *** goal is to recover the corresponding quadratic objective function using noisy ***,the iden...
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In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is *** goal is to recover the corresponding quadratic objective function using noisy ***,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 ***,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 *** formulate the problem as a risk minimization problem and approximate the problem using empirical *** is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative *** 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 *** efectiveness of our results are demonstrated by numerical examples.
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