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In this paper, based on combined Type-II censored samples, an exponential form for the underlaying distributions is considered for estimating the unknown parameters using the maximum likelihood and Bayesian methods. Three loss functions are used to derive the Bayesian estimators. Also, the Bayesian prediction for the order statistics from a future sample is calculated. Moreover, the results of the exponential and Pareto distributions are presented as illustrative examples. Finally, for illustrating all the inferential methods discussed in this paper, Monte Carlo simulation and data analysis for the exponential distribution are presented. [ABSTRACT FROM AUTHOR]

In this paper, a general exponential form of the underlying distribution and a general conjugate prior are used to discuss the maximum likelihood and Bayesian estimation based on an adaptive progressive censored sample. A general procedure for deriving the point and interval Bayesian prediction of the future progressive censored from the same sample as well as that from an unobserved future sample is also developed. The Weibull, Pareto, and Burr Type-XII distributions are then used as illustrative examples. Finally, two numerical examples are presented for illustrating all the inferential procedures developed here. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian approaches when samples are observed under progressive type-I interval censoring. Under classical approach we employ the stochastic expectation maximization algorithm to obtain maximum likelihood estimators for the unknown parameters and also compute associated interval estimates. Further under Bayesian approach we obtain Bayes estimators with respect to different symmetric, asymmetric and balanced loss functions. In this regard we use Tierney–Kadane and Metropolis–Hastings (MH) algorithm. For illustration purpose we analyse a real data set and conduct a Monte Carlo simulation study to observe the performance of the proposed estimators. Finally we present a discussion on inspection times and optimal censoring. [ABSTRACT FROM PUBLISHER]

This paper studies the problem of pilot-aided joint carrier frequency offset (CFO) and channel estimation using Fisher and Bayesian approaches in orthogonal frequency division multiplexing (OFDM) transmissions over time- and frequency-selective (doubly selective) channels. In particular, the recursive-least-squares (RLS) and maximum-likelihood (ML) techniques are used to facilitate the Fisher estimation implementations. For the Bayesian estimation, the maximum-a-posteriori (MAP) principle is employed in formulating the joint estimation problem. With known channel statistics, the MAP-based estimation is expected to provide better performance than the RLS- and ML-based ones. To avoid a possible identifiability issue in the joint estimation problem, various basis expansion models (BEMs) are deployed as fitting parametric models for capturing the time-variation of the channels. Numerical results and related Bayesian Cramér Rao bounds (BCRB) demonstrate that the deployment of BEMs is able to alleviate performance degradation in the considered estimation techniques using the conventional block-fading assumption over time-varying channels. Among the considered schemes, the MAP-based estimation using the discrete prolate spheroidal (DPS) or Karhuen Loève (KL) basis functions would be the best choice that can provide mean-squared-error (MSE) performance comparable to BCRB in low signal-to-noise ratio (SNR) conditions (e.g., coded OFDM transmissions). [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper outlines a general methodology for estimating the parameters of financial models commonly employed in the literature. A numerical Bayesian technique is utilised to obtain the posterior density of model parameters and functions thereof. Unlike maximum likelihood estimation, where inference is only justified in large samples, the Bayesian densities are exact for any sample size. A series of simulation studies are conducted to compare the properties of point estimates, the distribution of option and bond prices, and the power of specification tests under maximum likelihood and Bayesian methods. Results suggest that maximum–likelihood–based asymptotic distributions have poor finite–sampleproperties. [ABSTRACT FROM AUTHOR]

In this paper, a competing risks model is considered under adaptive type-I progressive hybrid censoring scheme (AT-I PHCS). The lifetimes of the latent failure times have Weibull distributions with the same shape parameter. We investigate the maximum likelihood estimation of the parameters. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) techniques to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. To evaluate the performance of the estimators, a simulation study is carried out. [ABSTRACT FROM AUTHOR]

In this paper, based on an adaptive Type-II progressively censored sample from the generalized exponential distribution, the maximum likelihood and Bayesian estimators are derived for the unknown parameters as well as the reliability and hazard functions. Also, the approximate confidence intervals of the unknown parameters, and the reliability and hazard functions are calculated. Markov chain Monte Carlo method is applied to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Moreover, results from simulation studies assessing the performance of our proposed method are included. Finally, an illustrative example using real data set is presented for illustrating all the inferential procedures developed here. [ABSTRACT FROM AUTHOR]

This paper develops Bayesian analysis in the context of progressively Type II censored data from the compound Rayleigh distribution. The maximum likelihood and Bayes estimates along with associated posterior risks are derived for reliability performances under balanced loss functions by assuming continuous priors for parameters of the distribution. A practical example is used to illustrate the estimation methods. A simulation study has been carried out to compare the performance of estimates. The study indicates that Bayesian estimation should be preferred over maximum likelihood estimation. In Bayesian estimation, the balance general entropy loss function can be effectively employed for optimal decision-making. [ABSTRACT FROM PUBLISHER]

Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure. [ABSTRACT FROM AUTHOR]

In this paper, based on a jointly type-II censored sample from two exponential populations, the Bayesian inference for the two unknown parameters are developed with the use of squared-error, linear-exponential and general entropy loss functions. The problem of predicting the future failure times, both point and interval prediction, based on the observed joint type-II censored data, is also addressed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the Bayesian estimators with the maximum likelihood estimator developed by Balakrishnan and Rasouli [Exact likelihood inference for two exponential populations under joint type-II censoring. Comput Stat Data Anal. 2008;52:2725–2738]. Finally, a numerical example is utilized for the purpose of illustration. [ABSTRACT FROM AUTHOR]

In this paper, maximum likelihood and Bayes estimators of the parameters, reliability and hazard functions have been obtained for two-parameter bathtub-shaped lifetime distribution when sample is available from progressive Type-II censoring scheme. The Markov chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the model parameters. It has been assumed that the parameters have gamma priors and they are independently distributed. Gibbs within the Metropolis–Hasting algorithm has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters as well as reliability and hazard functions have been computed. The results of Bayes estimators are obtained under both the balanced-squared error loss and balanced linear-exponential (BLINEX) loss. Moreover, based on the asymptotic normality of the maximum likelihood estimators the approximate confidence intervals (CIs) are obtained. In order to construct the asymptotic CI of the reliability and hazard functions, we need to find the variance of them, which are approximated by delta and Bootstrap methods. Two real data sets have been analyzed to demonstrate how the proposed methods can be used in practice. [ABSTRACT FROM AUTHOR]

The problem of estimating the reliability parameter R=Pr(Y < X) originated in the context of reliability where X represents the strength subjected to a stress Y. But traditionally it is assumed that the available data from the stress and strength populations are performed in exact numbers. However, some collected data might be imprecise, and are represented in the form of fuzzy numbers. In this paper, we consider the estimation of the stress-strength parameter R, when X and Y are statistically independent exponential random variables, and the obtained data from both distributions are reported in the form of fuzzy numbers. We consider the classical and Bayesian approaches. In the Bayesian setting, we obtain the estimate of R by using the approximation forms of Lindley, and Tierney & Kadane, as well as a Markov Chain Monte Carlo method under the assumption of statistically independent gamma priors. The estimation procedures are discussed in detail, and compared via Monte Carlo simulations in terms of their average values and mean squared errors. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a new model based on Burr X and Fréchet distributions for extreme values and derive some of its properties. Maximum likelihood estimation along with asymptotic confidence intervals is considered for estimating the parameters of the distribution. We demonstrate empirically the flexibility of the distribution in modeling various types of real data. Furthermore, we also provide Bayes estimators and highest posterior density (HPD) intervals of the parameters of the distribution using Markov Chain Monte Carlo (MCMC) methods. [ABSTRACT FROM AUTHOR]

In information theory, Kullback-Leibler divergence measure is a commonly used difference measure that is used for computing the distance between two probability distributions. In this paper, we apply Kullback-Leibler divergence measure between actual and approximate distribution to drive a loss function. We then apply the derived loss function on Exponential distribution to find the Bayes estimate of the parameter ϑ, and compare it with the Bayes estimate obtained using square error loss function. Our comparisons between these two estimates are based on complete, type II censoring and type I censoring data. [ABSTRACT FROM AUTHOR]

With subway systems around the world experiencing increasing demand, measures such as passengers left behind are becoming increasingly important. This paper proposes a methodology for inferring the probability distribution of the number of times a passenger is left behind at stations in congested metro systems using automated data. Maximum likelihood estimation (MLE) and Bayesian inference methods are used to estimate the left behind probability mass function (LBPMF) for a given station and time period. The model is applied using actual and synthetic data. The results show that the model is able to estimate the probability of being left behind fairly accurately. [ABSTRACT FROM AUTHOR]

In this paper, Burr-X distribution with Type-I hybrid censored data is considered. E-Bayesian estimation (expectation of the Bayesian estimate) and the corresponding maximum likelihood and Bayesian estimation methods are discussed for the distribution parameter and the reliability function. Bayesian and E-Bayesian estimates are derived by using LINEX and squared error loss (SEL) functions. By applying Markov chain Monte Carlo (MCMC) techniques Bayesian and E-Bayesian estimates are obtained. An illustrative examples of Type-I hybrid censored samples and real data set are presented. Finally, a comparison among the proposed estimation methods is conducted. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to suggest and study a new exponentiated general class (EGC) of distributions. Maximum likelihood, Bayesian and empirical Bayesian estimators of the parameter of the EGC of distributions based on lower record values are obtained. Furthermore, Bayesian prediction of future records is considered. Based on lower record values, the exponentiated Weibull distribution, its special cases of distributions and exponentiated Gompertz distribution are applied to the EGC of distributions. [ABSTRACT FROM AUTHOR]

This paper describes the frequentist and Bayesian estimation for the scale parameter λ and shape parameter β of the inverse Weibull (IW) distribution based on adaptive type-II progressive hybrid censoring scheme (AT-II PHCS). We discuss the maximum likelihood estimators (MLEs) and the approximate MLEs, where the MLEs cannot be obtained in closed forms. The Bayes estimates for the IW parameters are obtained based on squared error (SE) loss function by using the approximation form of Lindley (1980). The optimal censoring scheme has been suggested using two different optimality criteria. A real life data set is used for illustration purpose. Finally, the different proposed estimators have been compared through an extensive simulation studies. [ABSTRACT FROM AUTHOR]

In this paper, the optimum test plan and statistical inference of 3-step stepstress accelerated life tests (SSALT) under progressive Type-I censoring is studied. It is assumed that the lifetime of a test unit follow a Weibull distribution with mean lifetime of a unit is a log-quadratic function of stress level. The maximum likelihood and Bayesian method are used to obtain the point and interval estimates of the model parameters under progressive Type-I censoring. The Bayes estimates are obtained using Markov Chain Monte Carlo (MCMC) simulation based on Gibbs sampling. The optimum 3-step SSALT plan under progressive Type-I censoring is developed by minimizing asymptotic variance of the maximum likelihood estimators of log of mean life at the design stress. Finally, the numerical study is presented to illustrate the proposed study. [ABSTRACT FROM AUTHOR]

In this paper, for Weibull subfamily of Morgenstern family, the joint density of the concomitants of generalized order statistics (GOS 's) is used to obtain the maximum likelihood estimates (MLE) and Bayes estimates for the distribution parameters. Applications of these results for concomitants of order statistics are presented. [ABSTRACT FROM AUTHOR]

In this paper, both maximum likelihood and Bayesian estimators for a partially accelerated step-stress life test model are considered using type II censored data from Pareto distribution of the second kind. The posterior means and posterior variances are obtained under the squared error (SE) loss function using Lindley's approximation procedure. The maximum likelihood estimators and analogous Bayes estimators are compared in terms of their mean-square errors based on simulated samples from Pareto distribution. [ABSTRACT FROM AUTHOR]

We address the problem of rapidly discovering spectrum opportunities for seamless service provisioning in cognitive radio networks (CRNs). In particular, we focus on multichannel communications via channel-bonding with heterogeneous channel characteristics of ON/OFF patterns, sensing time, and channel capacity. Using dynamic programming (DP), we derive an optimal online sensing sequence incurring a minimal opportunity-discovery delay, and propose a suboptimal sequence that presents a near-optimal performance while incurring significantly less computational overhead than the DP algorithm. To facilitate fast opportunity discovery, we also propose a channel-management strategy that maintains a list of backup channels to be used at building the optimal sequence. A hybrid of maximum likelihood (ML) and Bayesian inference is introduced as well for flexible estimation of ON/OFF channel-usage patterns, which selectively chooses the better between the two according to the frequency of sensing and ON/OFF durations. The performance of the proposed schemes, in terms of the opportunity-discovery delay, is evaluated via in-depth simulation, and for the scenarios we considered, the proposed suboptimal sequence achieves a near-optimal performance with only an average of 0.5 percent difference from the optimal delay, and outperforms the previously proposed probabilistic scheme by up to 50.1 percent. In addition, the backup channel update scheme outperforms the no-update case by up to 49.9 percent. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, and based on a progressive type-II censored sample from the generalized Rayleigh (GR) distribution, we consider the problem of estimating the model parameters and predicting the unobserved removed data. Maximum likelihood and Bayesian approaches are used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are used to predict the life lengths of the removed units in multiple stages of the progressively censored sample. Artificial and real data analyses have been performed for illustrative purposes. [Copyright &y& Elsevier]

Bayesian estimation of the parameters in beta mixture models (BMM) is analytically intractable. The numerical solutions to simulate the posterior distribution are available, but incur high computational cost. In this paper, we introduce an approximation to the prior/posterior distribution of the parameters in the beta distribution and propose an analytically tractable (closed form) Bayesian approach to the parameter estimation. The approach is based on the variational inference (VI) framework. Following the principles of the VI framework and utilizing the relative convexity bound, the extended factorized approximation method is applied to approximate the distribution of the parameters in BMM. In a fully Bayesian model where all of the parameters of the BMM are considered as variables and assigned proper distributions, our approach can asymptotically find the optimal estimate of the parameters posterior distribution. Also, the model complexity can be determined based on the data. The closed-form solution is proposed so that no iterative numerical calculation is required. Meanwhile, our approach avoids the drawback of overfitting in the conventional expectation maximization algorithm. The good performance of this approach is verified by experiments with both synthetic and real data. [ABSTRACT FROM AUTHOR]

In this article likelihood and Bayesian estimations for the partially accelerated constant-stress life test model are compared using Type-II censored data from the Pareto distribution of the second kind. The posterior means and posterior variances are obtained under the squared error loss function using Lindley's approximation procedure. Furthermore, the highest posterior density credible intervals of the model parameters based on Gibbs sampling technique are presented. For illustration, simulation studies are provided. It is shown with the Bayesian approach via Gibbs sampling procedure that the statistical precision of parameter estimation is improved. Consequently, the required number of failures could be reduced. That is, more savings in time and cost can be achieved through the Markov chain Monte Carlo (MCMC) technique. Reducing the total testing time and the total number of failures without sacrificing much of the statistical power in inference is often desired in industrial applications. [ABSTRACT FROM AUTHOR]

A four-parameter extended fatigue lifetime model called the odd Birnbaum-Saunders geometric distribution is proposed. This model extends the odd Birnbaum-Saunders and Birnbaum-Saunders distributions. We derive some properties of the new distribution that include expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood and a Bayesian approach are adopted to estimate the model parameters; in addition, various simulations are performed for different parameter settings and sample sizes. We propose two new models with a cure rate called the odd Birnbaum-Saunders mixture and odd Birnbaum-Saunders geometric models by assuming that the number of competing causes for the event of interest has a geometric distribution. The applicability of the new models are illustrated by means of ethylene data and melanoma data with cure fraction. [ABSTRACT FROM AUTHOR]

This article deals with the Bayesian and non Bayesian estimation of multicomponent stress–strength reliability by assuming the Kumaraswamy distribution. Both stress and strength are assumed to have a Kumaraswamy distribution with common and known shape parameter. The reliability of such a system is obtained by the methods of maximum likelihood and Bayesian approach and the results are compared using Markov Chain Monte Carlo (MCMC) technique for both small and large samples. Finally, two data sets are analyzed for illustrative purposes. [ABSTRACT FROM PUBLISHER]

The use of finite mixture distributions, to control for unobserved heterogeneity, has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive reparability of the log likelihood function. In this research, Bayesian estimators have been obtained for the parameters of the mixture of exponentiated Weibull distribution when sample is available from censoring scheme. The maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been obtained by Elshahat and Mahmoud (2016). Bayes and approximate Bayes (Lindley's form) estimators have been developed under squared error loss function as well as under LINEX loss function using non-informative type of priors for the parameters will be obtained. A numerical illustration for these new results is given. [ABSTRACT FROM AUTHOR]

This article compares likelihood and Bayesian estimations for partially accelerated constant-stress life test model under type II censoring assuming Pareto distribution of the second kind. Both maximum likelihood and Bayesian estimators of the model parameters are derived. The posterior means and posterior variances are obtained under the squared error loss function using Lindley's approximation procedure. The advantages of this proposed procedure are shown. Monte Carlo simulations are conducted under different samples sizes and different parameter values to assess and compare the proposed methods of estimation. A noninformative prior on the model parameters is used to make the comparison more meaningful. It has been observed that Lindley's method usually provides posterior variances and mean squared errors smaller than those of the maximum likelihood estimators. That is, Lindley's method produces improved estimates, which is an advantage of this method. [ABSTRACT FROM AUTHOR]