Publications (21)23.05 Total impact
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ABSTRACT: Bayesian estimates of the parameter p and the reliability function for the twoparameter Burr type XII failure model under three different loss functions, absolute difference, squared error and logarithmic are derived. It is assumed that the parameter p behaves as a random variable having (i) a gamma prior and (ii) a vague prior. Monte Carlo simulations are presented to compare the Bayesian estimators and the maximum likelihood estimators of the parameter p and the reliability function. The results show that the “popular” squared error loss function is not always the best, and that the other loss functions give comparable results.  [Show abstract] [Hide abstract]
ABSTRACT: The lognormal distribution with density function formula presented is considered as a failure model from the Bayesian point of view. The shortest Bayesian confidence intervals for the parameters and reliability function are obtained for two cases. First, it is assumed that σ2 is known and that γ has a normal prior distribution. Then, the case that γ is known and σ2 has an inverted gamma prior distribution is considered. Some computer simulations are given to demonstrate the advantage of the shortest Bayesian confidence intervals over the ordinary Bayesian confidence intervals in terms of their length ratios. 
Article: On the test of Liu and Chow's procedure for assessing equivalence in variability of bioavailability
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ABSTRACT: Similar to Schuirmann's two onesided tests procedure for assessment of bioequivalence in average bioavailability (Schuirmann,), Liu and Chow proposed a two onesided tests procedure for assessment of equivalence of variability of bioavailability. Their procedure is derived based on the correlation between crossover differences and subject totals. In this paper, we examined the performance of their test procedure in terms of its test size and power for various situations where the intersubject variability and the intrasubject variability of the test drug product are relatively larger, similar, and smaller than that of the intrasubject variability of the reference drug product.  [Show abstract] [Hide abstract]
ABSTRACT: The exponentialmultinomial distribution arises from: (1) observing the system failure of a series system with p components having independent exponential lifetimes, or (2) a competingrisks model with p sources of failure, as well as (3) the MarshallOlkin multivariate exponential distribution under a series sampling scheme. Hierarchical Bayes (HB) estimators of the component subsurvival function and the system reliability are obtained using the Gibbs sampler. A largesample approximation of the posterior pdf is used to derive the HB estimators of the parameters of the model with respect to the quadratic loss function. The exact risk of the HE estimator is obtained and is compared with those corresponding to some other estimators such as Bayes, maximum likelihood, and minimum variance unbiased estimators  [Show abstract] [Hide abstract]
ABSTRACT: In some situations a small proportion of data do not arise from a given Poisson distribution but from a Poisson distribution with a different parameter value. The nonBayesian and Bayesian outlier detection rules are proposed based on the square root transformed data. Different trimmed means are formed according to the above mentioned outlier detection methods. The relative efficiencies of these estimators with respect to the sample mean, and the mean proportions of data classified as outliers are computed by using Monte Carlo methods. Based on the computer simulation we can conclude that the nonBayesian estimators are good robust estimators.  [Show abstract] [Hide abstract]
ABSTRACT: Two important, to scientist and engineers, regression fitting procedures, namely the least squares (LS) and the total least squares (TLS) methods and their general randomerror analysis are described. The firstorder random errors of the slope and yintercept of the line using the above mentioned procedures are derived in detail under the assumption that the variancecovariance matrix exists for the random error vector. With the additional bivariate normal error distribution assumption, the Maximum Likelihood (ML) estimators and their standard deviations are also derived. The effectiveness of these procedures is studied through computer simulation.  [Show abstract] [Hide abstract]
ABSTRACT: We determine the Bayes estimator of the reliability function for a hierarchical Weibull failure model, assuming the scale parameter is known, and treating the shape parameter, α, as stochastic. The shape parameter is generated from a mixture containing a point mass at α = 1, yielding exponential data, and cx distributed as Beta Type 11, yielding general Weibull data. The estimator is then evaluated for data from a series of different failure distributions, including the parent model, and simple exponential and simple Weibull models. Its robustness is measured by evaluating the root mean squared errors of the mixture estimator and comparing them to root mean squared errors for some competing models.  [Show abstract] [Hide abstract]
ABSTRACT: A stochastic model for biochemical oxygen demand (BOD) and dissolved oxygen (DO) at a distance t downstream, when pollutants are discharged over a continuous stretch, is a random differential equation of the form , with the initial condition X0 = X(0). Assuming that X0 is a random vector having a bivariate normal distribution with the mean vector μ0 and the precision (the inverse of the variancecovariance) matrix Λ0, we provide the prediction equation at any point t a for μ0 keeping Λ0 fixed and known, and (ii) a normalWishart prior for (μ0, Λ0. The theory is supplemented by numerical studies.  [Show abstract] [Hide abstract]
ABSTRACT: Confidence bounds for the parameter and the reliability function are derived for the exponential failure model, from the hierarchical Bayesian view. The parameter of the exponential is considered as a random variable with a gamma function as a prior. Furthermore, the scale parameter of the gamma prior is assumed to be a random variable with a uniform as a hyperprior. Under these assumptions confidence bounds are derived for the exponential parameter and reliability function. Monte Carlo simulation is utilized to compare the classical confidence bounds to the hierarchical Bayes. 
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ABSTRACT: Bayes estimators for the probability of “success” and the reliability function of the zerotruncated, binomial and negative binomial distributions are obtained. Furthermore, recurrence relations for the estimators of the probability of “success” are also derived. 
Article: The zerotruncated negative binomial distribution as a failure model from the Bayesian approach
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ABSTRACT: The zerotruncated negative binomial distribution is considered as a failure model from the Bayesian point of view. It is assumed that the location parameter is a stochastic variable with beta as its prior distribution. Under this assumption Bayes estimators are derived for the location parameter and reliability function. By means of Monte Carlo Simulation the minimum variance unbiased estimators (MVUEs) for the parameter and reliability function are compared to the corresponding Bayes estimators.  [Show abstract] [Hide abstract]
ABSTRACT: Suppose R is the strength of a component subject to a stress S, where S and R have distribution F and G respectively. A Monte Carlo comparison of the Bayes estimators of the reliability parameter P(S < R), the probability that the strength exceeds the stress, of the component, when F and G are independent Dirichlet processes, with corresponding rival estimators such as the maximum likelihood estimators and the usual Ustatistic is considered. The results show that the Bayes estimators are superior to the rival estimators in the sense of the smaller root mean squared errors.  [Show abstract] [Hide abstract]
ABSTRACT: Recently, Hannan studied the resolution of closely adjacent spectral lines. In the paper, he discusses the problem of determining the parameters of a trigonometric polynomial when it is observed with stationary noise. He also obtains the asymptotic properties of the estimates of these parameters. The purpose of this paper is to fit a trigonometric polynomial to a Biochemical Oxygen Demand (BOD) data set and to examine the sampling properties of the estimates of the parameters of the model by using the empirical bootstrap procedure. In particular, 95% bootstrap confidence intervals of the estimates are obtained. We also employ the Bayesian bootstrap technique to obtain the interval estimates of the parameters. The problem of prediction using the empirical and Bayesian bootstrap procedures is also studied. This model, when compared with time series models of the form ARIMA (p, d, q), gives better fit in terms of a lower mean squared error (MSE).  [Show abstract] [Hide abstract]
ABSTRACT: In this presentation the logorithmic series is studied as a failure model from the Bayesian point of view. It is assumed that the location parameter behaves as a random variable with beta as its prior distribution. Based on this assumption Bayes estimators for the location parameter and reliability function are derived. By using computer simulation we compare the Bayes estimator for the parameter with the corresponding minimum variance unbiased estimator (MVUE) and the Bayes estimator for the reliability with a corresponding unbiased estimator derived from the MVUE of the probability function.  [Show abstract] [Hide abstract]
ABSTRACT: Suppose n items, each consisting of p components, are put on test and that testing is continued until some preassigned time point τ0. An item fails if any one of its p components fail. Assume that the component life lengths are independent and each life time is exponentially distributed. The Bayes estimation of the parameter of the failure distribution of each component is carried out by using independent gamma and uniform prior densities for the parameters of failure distributions. The estimation of the reliability function of an item is also carried out. A Monte Carlo simulation is performed in order to compare the Bayes and maximum likelihood estimators of the parameters and the reliability function. Computations indicate that the Bayes estimators are better than the maximum likelihood estimators in the sense of smaller root mean squared errors.  [Show abstract] [Hide abstract]
ABSTRACT: A twocomponents parallel or series system is studied where the failure time of each component follows the Burr distribution. The testing environment of the system is assumed different from the operating one, causing the parameters p i (i=1,2) to increase or decrease by a positive, random amount η. Two priors are considered for the behaviour of η, a gamma and a uniform. The Bayesian reliability is derived in closed form. Three hypothetical examples show how this approach could be used by reliability engineers. 
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ABSTRACT: A failure population need not be homogeneous. It can be a mixture of two or more distinct subpopulations. In this paper a population which can be divided into two subpopulations each representing a different cause of failure, is considered. The subpopulations each follow a Weibull distribution. Maximum likelihood estimators, Bayes estimators with respect to proper priors, and with respect to improper priors for the population parameters and the reliability function are derived. All analysis is based on samples censored at a predetermined test termination time. A comparison of the Bayes estimation and the maximum likelihood estimation is made through Monte Carlo simulation.  [Show abstract] [Hide abstract]
ABSTRACT: A nonparametric probability estimator, having a uniform biochemicaloxygen demand kernel, is utilized to obtain the joint probability density function of (BOD) and dissolved oxygen (DO) along the stretch of a stream when the pollutant is discharged over an interval and the velocity is distancedependent. Furthermore, probabilistic confidence bounds for BOD and DO are derived. An example and computations are presented to illustrate the usefulness of the model.
Publication Stats
56  Citations  
23.05  Total Impact Points  
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Institutions

19872000

University of North Carolina at Charlotte
 Department of Mathematics & Statistics
Charlotte, North Carolina, United States
