Bayesian estimation of the scale parameter of inverse. The probability density function of rayleigh distribution is. Thats because the parameter in the example is assumed to take on only two possible values, namely. We hope wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly. In section 4, classical and bayesian prediction intervals are obtained. Zellnerbayesian estimation and prediction using asymmetric loss functions. Estimation and prediction based on krecord values from normal distribution. Bayesian estimation of the scale parameter of inverse weibull distribution under the asymmetric loss functions farhadyahgmaei,manoochehrbabanezhad,andomids. Bayesian estimation for the pareto income distribution.
Journal of american statistical association, 81 394. Journal of the american statistical association 81. In this paper bayes estimation of the reliability function of the lomax distribution have been obtained by taking noninformative and beta prior distributions. Reliability estimation in maxwell distribution with typeii censored data. Inadmissibility of the usual estimators of scale parameters in problems with unknown location and scale parameters. Bayesian estimation and prediction using asymmetric loss functions. Moghadam department of statistics, faculty of sciences, golestan university, gorgan, golestan, iran correspondence should be addressed to manoochehr babanezhad. Bayesian modeling and inference for asymmetric responses. Bayesian estimation of the parameter and reliability function of an. However, for some estimation and prediction problems, the real loss function is often not symmetric.
We also obtain the bayes estimators of the reliability function using both symmetric as well as asymmetric loss functions and compare its performance based on a monte carlo simulation study. Bayesian inference using record values from rayleigh model. Introduction to bayesian decision theory parameter estimation problems also called point estimation problems. The results of this paper provide a link between the robust bayesian analysis for the normal. Bayesian estimation of the parameter and reliability. Also, cis of mles and cris of bayesian and ebayesian estimates are constructed. Bayesian inference of the weibull model based on interval. With known shift point m, the bayes estimator on befor and after shift process means. Bayesian and frequentist estimation and prediction for. The bayes estimators are obtained under the symmetric squared error and the asymmetric linear exponential loss functions using noninformative and reciprocal gamma priors. Bayesian estimation and prediction for the generalized lindley distribution under asymmetric loss function sanjay kumar singh, umesh singh and vikas kumar sharma. It is shown that some usual estimators, for example, a scalar sample mean or a scalar least squares regression coefficient.
Pdf bayesian estimation and prediction of discrete. In the next section a decision theoretic approach is discussed, which is followed. Pdf a nonlinear exponentialnlinex loss function in. The maximum likelihood estimators for the shape parameter and scale parameter are obtained. Bayesian estimation and prediction of discrete gompertz distribution. Bayesian inference and prediction for normal distribution. An asymmetric loss function is a model that defines unequal loss to the. Generalized lindley distribution, loss functions, bayes estimator, hpd intervals, bayes. Efficient empirical bayes prediction under check loss using. On a bayesian aspect for soft wavelet shrinkage estimation. Finally, under a latent variable formulation, we use a generalized extreme value gev link to model multivariate asymmetric spatiallycorrelated binary responses that also exhibit nonrandom missingness, and show how this proposal improves inference over other popular alternative link functions in terms of bias and prediction.
Bayesian prediction of deterministic functions, with. Soft gaussian cde regression models and loss functions. Real estate price prediction under asymmetric loss. Bayesian estimation of the shape parameter of the generalised. The probability density function pdf of oneparameter burrx distribution is given by. Alsaleh and muttlak 10 obtained the bayesian estimates of the exponential distribution. Bayesian and non bayesian method of estimation of scale. An approximation based on the laplace approximation method tierney and kadane, 1986 is used for obtaining the bayes estimators of the parameters and reliability function.
The present paper proposes some bayes estimators of shape parameter of pareto income distribution in censored sampling. Asymmetric loss functions have been shown to be functional, see varian 1975, zellner 1986. We have also considered the bayesian approach in estimating the weibull parameters with intervalcensored data under three loss functions. Inference based on krecord values from generalized. Weibullbayesian estimation based on maximum ranked set sampling with. Journal of statistical planning and inference, 29, pp. The loss function used is squared error, linex, precautionary and entropy. For c 1, equation 4 provides the bayes estimator under. Yarmohammadi 24studied the classical and bayesian estimations on the generalized exponential distribution using censored data. The paper starts with a short summary on bayesian parameter estimation and credibility intervals. Pdf bayesian estimation for rayleigh distribution based.
We assess our proposed method via simulation studies and. Estimation of the binomial parameter n using a linex loss. Pdf bayesian estimation and prediction for the generalized. Prediction problems involving asymmetric loss functions arise routinely in many fields, yet the theory of optimal prediction under asymmetric loss is not well developed. Robust bayesian estimation and prediction of reserves in exponential model with quadratic variance function.
In section 3, we obtain the bayes estimators of and risk functions under symmetric and asymmetric loss functions. Bayesian estimation of the reliability function of the. Asymmetric loss functions and sample size determination. Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments carla currin, toby mitchell, max morris, and don ylvisaker this article is concerned with prediction of a function yt over a multidimensional domain t. Zellner a 1994 bayesian and nonbayesian estimation using balanced loss functions. Bayesian estimation of the parameter of maxwell distribution under different loss functions. The bayes estimates of the parameters are also developed by using markov chain monte carlo method under symmetric and asymmetric loss functions. In the case where the parameter space for a parameter. Abstract estimators and predictors that are optimal relative to varians asymmetric linex loss function are derived for a number of wellknown models. Bayesian point prediction is co nsidered under two types o f loss func tions. Rayleigh distribution ird with probability density function pdf and the. Bayesian estimation of a normal mean parameter using the linex. Bayes estimator, linear exponentiallinex loss function.
Bayes estimation and prediction using asymmetric loss functions. Bayesian modeling and inference for asymmetric responses with applications. Bayesian estimation and prediction for the generalized lindley distribution under asymmetric loss function. For full access to this pdf, sign in to an existing account, or. Bayesian estimation and prediction using asymmetric loss. International journal of science and research, vol. Efficiencies of the proposed bayes estimators are obtained with respect.
Bayesian estimators of gini index and a poverty measure are obtained in case of pareto distribution under censored and complete setup. Bayesian inference using record values from rayleigh model with application. We study the optimal prediction problem under general loss structures and characterize the optimal predictor. As mentioned earlier, when 0 has a normal posterior pdf, say with mean m. Finally, a numerical study is provided to illustrate the results. Loss function estimation of forecasting models a bayesian. A bayesian estimation of reliability model using the linex. Bayesian estimation and prediction using asymmetric loss functions arnold zellner estimators and predictors that are optimal relative to varians asymmetric linex loss function are derived for a number of wellknown models. In section 2, we discuss prior and loss functions used in our bayesian estimation. Moghadam departmentofstatistics,facultyofsciences,golestanuniversity,gorgan49815739,golestan,iran.
Their risk functions and bayes risks are derived and compared with those of usual estimators and predictors. Other loss functions another possible loss function, though less widelyused, is the linexloss function, varian 1975, zellner 1986 jasa, \ bayesian estimation and prediction using asymmetric loss functions. Estimation of the binomial parameter n using a linex loss function. Loss function estimation of forecasting models a bayesian perspective frank schorfheide university of pennsylvania, department of economics. Takada and nagata 1995 proposed a fixedwidth sequential confidence interval for the mean of a gamma distribution and norstrom 1996 provided the.
Weibullbayesian estimation based on maximum ranked set. Bayesian approach to life testing and reliability estimation using a symmetric loss function. A number of authors have considered bayesian and nonbayesian estimation and prediction problems for the rayleigh distribution using different types of censoring and noncensoring data. Optimal prediction under asymmetric loss econometric. Asymmetric linex loss function has been considered to study the effects of overestimation and underestimation.
Bayesian and robust bayesian analysis under a general. The use of asymmetric loss functions gives us the possibility to differentiate. Bayesian estimation and prediction using asymmetric loss functions, jour. Read bayesian inference using record values from rayleigh model with application, european journal of operational research on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. In this paper, the problem of bayesian estimation of flood quantiles is studied.
Symmetry free fulltext ebayesian estimation based on. It is shown that some usual estimators, for example, a scalar sample mean or a scalar least squares regression coefficient estimator. Bayesian estimation and prediction using asymmetric loss functions, journal of the american statistical. Bayesian estimation of twoparameter weibull distribution. Estimation and prediction using asymmetric loss functions 447. Available formats pdf please select a format to send. The performance of the estimators is assessed on the basis of their biases and relative. A number of asymmetric loss functions have been shown to be functional, see varian 1975, zellner 1986, chandra 2001 etc. Bayesian and e bayesian method of estimation of parameter. Also there has been a wide range of discussion about the impact of using asymmetric loss functions in bayesian estimation and prediction. Estimation and testing of forecasting rationality under flexible loss.
Bayesian estimation and prediction for the generalized lindley. Finally, a simulation study is performed to find the performance of different estimators developed in this paper. The bayes estimate of under self is the posterior mean of. Bayesian estimation and prediction for the generalized. Based on sel and linex loss functions, bayesian and ebayesian estimates are derived. Theoretical developments for prediction under each loss function in the presence of normal errors are presented and useful tables of adjustment factor values given. Bayesian estimation and prediction using asymmetric loss function. The said estimators are obtained using two noninformative priors, namely, uniform prior and jeffreys prior, and one conjugate prior under the assumption of linear exponential linex loss function. As mentioned earlier, when 0 has a normal posterior pdf, say with mean. Bayesian estimation of reliability function for a changing. In the present paper, we consider the above loss functions for better comparison of bayesian analysis. Other loss functions another possible loss function, though less widelyused, is the linexloss function, varian 1975, zellner 1986 jasa, \bayesian estimation and prediction using asymmetric loss functions. Bayesian estimation of inequality and poverty indices in. Pandey and rai 1992 considered bayesian estimation of mean and square of mean of.
Statistical prediction analysis under asymmetric loss functions in fixed. Bayesian estimation and prediction for the inverse rayleigh lifetime distribution. Bayesian and robust bayesian analysis under a general class of balanced loss functions. Prediction under generalized exponential distribution. This study became necessary because of the limited discussion in the literature, if at all, with regard to estimating the weibull parameters with intervalcensored data using bayesian. Otherwise one has to use asymmetric loss functions. In this paper, bayes estimates for the parameters k, c and reliability function of the burr type xii model based on a type ii censored samples under asymmetric loss functions viz. In this paper the problem of bayes estimation of the reliability and the shape parameter p of a finite range failure time model is considered assuming scale parameter. Estimation of mean and its function using asymmetric loss.
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