In this study various types of loss functions and their uses were studied. Estimation and prediction based on krecord values from normal distribution. Bayesian inference and prediction for normal distribution. In this paper bayes estimation of the reliability function of the lomax distribution have been obtained by taking noninformative and beta prior distributions. Weibullbayesian estimation based on maximum ranked set. A more appropriate asymmetric loss function, general entropy loss function gelf is in. For example, in the estimation of reliability and failure rate functions, an overestimation is usually much more serious than an underestimation. 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. Bayesian estimation based on ranked set sampling using asymmetric loss function 1a. Zellner, a bayesian estimation and prediction using asymmetric loss functions, journal of the american statistical association, 81, 446451 1986 147. Point estimation under asymmetric loss functions for left.
Optimal prediction under asymmetric loss econometric. Bayesian analysis of rayleigh distribution under quasi. Zellner 21 introduced bayesian estimation by using asymmetric loss function. Bayesian estimation in this section, we will obtain the bayes estimates of the shape parameter t and the hazard function ht of the gompertz distribution by considering symmetric loss function self and three asymmetric loss functions qlf, elf and llf.
Estimators and predictors that are optimal relative to varians asymmetric linex loss function are derived for a number of wellknown models. 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. Bayesian estimation and prediction using asymmetric loss functions created date. Ebayesian prediction for the burr xii model based on type. Ir, spec ifying the cost that is incurred when the true state of nature is s and the chosen decision is a.
Linex loss function as an asymmetric blf to derive the bayes predictions of the future krecords in. In this paper, we use the linex loss function to derive the bayesian estimate of the parameter of the exponential distribution based on ranked set sampling. Bayesian estimation of reliability function for a changing. Bayesian estimation and prediction for the generalized. With rightskewed functions an increase of the loss ratio sosu reduces the coverage. Bayesian estimation based on ranked set sampling using asymmetric loss function. Keynes as a result of my recent post on bayesian estimation of a simple consumption function, a few people emailed asking for proofs of the results that the bayes estimator is the mean a median a mode of the posterior density, when the loss function is quadratic absolute error zeroone. Bayes estimation under asymmetric loss functions the bayesian inference procedures have l. Abstract estimators and predictors that are optimal relative to varians asymmetric linex loss function are derived for a number of wellknown models. A modification of ranked set sampling rss called maximum ranked set sampling with unequal sample mrssu is considered for the bayesian estimation of scale parameter. Under this method, we use linex loss function, conjugate and jeffreys prior distributions to derive the bayesian estimate of in order to measure the efficiency of the obtained bayesian. Bayesian and ebayesian method of estimation of parameter.
In some situation overestimation is more serious than under estimation or viceversa. Bayesian estimation of the weibull parameters based on competing risks grouped data. Bayesian estimation of the shape parameter of the generalised exponential distribution under different loss functions. Bayesian estimation of reliability function for a changing exponential family model under different loss functions. This loss function is a generalization of the entropy loss function used by several authors where the shape parameter cis taken equal to 1. Bayesian and frequentist estimation and prediction for. Bayesian estimation and prediction using asymmetric loss functions.
The loss function used is squared error, linex, precautionary and entropy. Bayesian estimation and prediction using asymmetric loss function. Asymmetric linex loss function has been considered to study the effects of overestimation and underestimation. We study the optimal prediction problem under general loss structures and characterize the optimal predictor. Bayesian estimation of the shape parameter of finite range distribution using linex loss function with type ii. Journal of the american statistical association, 894. Journal of statistical planning and inference 29 1991 21 21 northholland bayesian approach to life testing and reliability estimation using asymmetric loss function a. 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. Comparison of estimates using censored samples from. 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. The effect on the change of coverage strongly depends on the skewness of the basic distribution function. In the current investigation, bayesian estimators under sel function for the parameters of pareto distribution are obtained based on srs and rss in two cases, one cycle rss and mcycle rss in section 2.
Moorhead and wu 1998, spiring and yeung 1998, chandra 2001, etc. In section 2, we discuss prior and loss functions used in our bayesian estimation. Bayesian analysis in econometrics pdf free download. Clearly self is a symmetrical loss function and assign losses to over estimation and underestimation. Finally, comparison between bayes and ebayes estimates have been made using simulation study in. In this study linex loss function, the analysts loss function, the optimal prediction under asymmetric loss, loss functions for forecasting financial returns, loss function and forecast biasedness. The probability density function of rayleigh distribution is.
E bayesian and bayesian predictive function approaches have been used for obtaining the estimates of the unknown parameter, and some other lifetime characteristics such as the reliability and hazard functions. Tiao g and tan w bayesian analysis of random effect models. Estimation of reliability function of lomax distribution. In section 3, e bayes estimate have also been obtained using three different prior distributions. Asymmetric loss functions are used to reflect that, in most situations of interest, overestimation of a parameter does not produce the same economic consequence than underestimation. In this paper, bayes estimates of the parameters and functions thereof in the lefttruncated exponential distribution are derived. Savage argued that using non bayesian methods such as minimax, the loss function should be based on the idea of regret, i.
In this paper the main objective was to implement the method of optimal estimating functions in volatility estimation and prediction using asymmetric garch modes. Yarmohammadi 24studied the classical and bayesian estimations on the generalized exponential distribution using censored data. Bayesian and e bayesian method of estimation of parameter. Prediction problems involving asymmetric loss functions arise routinely in many fields, yet the theory of optimal prediction under asymmetric loss is not well developed. Estimation for the parameter of poissonexponential. It is shown that some usual estimators, for example, a scalar sample mean or a scalar least squares regression coefficient estimator, are inadmissible relative to asymmetric linex loss by providing alternative estimators that dominate them uniformly in terms of risk. Journal of the american statistical association, 1986. Bayesian estimation of the reliability function of the. Also there has been a wide range of discussion about the impact of using asymmetric loss functions in bayesian estimation and prediction. The bayes estimator under the above loss function, say, is the. 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. Asymmetric loss functions and sample size determination.
Implementation of the estimating functions approach in. Box 2455, riyadh 11451, saudi arabia 3department of mathematics and statistics, mcmaster university. Inadmissibility of the usual estimators of scale parameters in problems with unknown location and scale parameters. This work is licensed under a creative commons attribuzione non commerciale. Basu department of statistics, university of missouri, columbia, mo 65211, usa nader ebrahimi department of mathematics, university of northern illinois, dekalb, il 60115, usa received 3 august 1989 abstract. Prediction under generalized exponential distribution. Robust bayesian estimation and prediction of reserves in exponential model with quadratic variance function. Reliability estimation in maxwell distribution with typeii censored data. Journal of statistical planning and inference, 29, pp. Asymmetric loss functions have been shown to be functional, see varian 1975, zellner 1986.
Bayesian estimation of inequality and poverty indices in. The general version 8 allows di erent shapes of the loss function to meet the practical needs. Theoretical developments for prediction under each loss function in the presence of normal errors are presented and useful tables of adjustment factor values given. In section 3, we obtain the bayes estimators of and risk functions under symmetric and asymmetric loss functions. Bayesian estimation of the parameter of maxwell distribution under different loss functions. 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. Both the noninformative prior and an informative prior on the reliability level. Based on type ii censored samples of size r obtained from a life test of n items. In this paper, bayesian and e bayesian method of estimation are proposed for estimating the parameter of rayleigh distribution. Bayesian estimators of gini index and a poverty measure are obtained in case of pareto distribution under censored and complete setup. This is not an indication of a security issue such as a virus or attack. Pdf estimation and prediction of inverse lomax model via.
Bayesian estimation of twoparameter weibull distribution. Estimation and prediction of inverse lomax model via bayesian approach. The present paper proposes some bayes estimators of shape parameter of pareto income distribution in censored sampling. Prediction of krecords from a general class of distributions under balanced type loss functions. It could be something as simple as a run away script or learning how to better use e. Pdf bayesian estimation and prediction of discrete. Bayesian inference of the weibull model based on interval.
In section 2, bayes estimate of parameter have been obtained using conjugate prior under linex loss function. Journal of american statistical association, 81 394. This is formally expressed via a loss function l s,a. In section 4, classical and bayesian prediction intervals are obtained. Real estate price prediction under asymmetric loss. Bayesian approach to life testing and reliability estimation using a symmetric loss function.
Nonetheless, it has been observed that in certain situations when one loss is the true loss function, bayes estimate under another loss function performs better. Bayesian estimation based on ranked set sampling using. Bayesian estimation and prediction for pareto distribution. Pdf bayesian estimation of the shape parameter of the.
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. Prediction using asymmetric loss functions let y be a future value of a variable with a given prediction pdf and assume that the following class of asymmetric linex loss functions is appropriate. Bayesian estimation has been developed under symmetric and asymmetric loss functions in. Section 4 is the asymmetric loss function which is divided into two subsections, that is, linear. Bayesian estimation of shape parameter of pareto income. Robust bayesian estimation and prediction of reserves in. In some situation overestimation is more serious than underestimation or viceversa. The bayes estimate of the parameter is derived under the assumption that the prior distribution is informative i. Bayesian estimation of the weibull parameters based on.
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