# efficient estimator for exponential distribution

As the access to this document is restricted, you may want to search for a different version of it. \$\endgroup\$ – André Nicolas Mar 11 '14 at 1:06 | … It turns out that the use of RSS and its suitable modifications results in much improved estimators compared to the use of a SRS. Proper-ties of the estimators are expressed in terms of almost sure convergence, asymptotic normality and Bayesian risks. This paper deals with preliminary test single stage Bayesian Shrinkage estimator for the scale parameter (θ) of an exponential distribution when a guess value (θ 0 ) for (θ) available from the past studies under the improper prior distribution and the quadratic loss function. Bayes Estimator for Exponential Distribution with Extension of Jeffery Prior Information Malaysian Journal of Mathematical Sciences 303 If we let 1 1 2 c = , 1 1 1 n i i B t n θ = = − ∑ which is Jeffrey estimator and it is a special case of our proposed method . An unbiased estimator of θthat attains the CRB for θfor all θin the parameter space Θ is said to be eﬃcient. Complement to Lecture 7: "Comparison of Maximum likelihood (MLE) and Bayesian Parameter Estimation" Furthermore, it maintains the high efficiency even for the heavy-tailed t 3 error distribution. Exponential distribution plays an important role in modeling real-life data relating to the continuous waiting time. endobj So, the estimators of the two-parameter exponential distribution are as follows: (3) (4) where and represent the Bayes estimators of the simple linear regression model. Estimator: A function of the sample observations used to to be an estimator. iii. I rewrote the computations as SAS/IML functions to make them more efficient … a push in … Find an unbiased estimator of B. Analytical expressions are derived for the bias and the mean squared error. ?����J��� g�G� N9Z����Hk��u Simulation studies and real data applications show that the maximum likelihood estimator performs better than others. (1972). Exponential class software reliability models , : dels which have exponential failure time distribution. 3 0 obj 2, pp. She also used RSS to estimate the correlation coefficient of a bivariate normal distribution. Homework Equations The Attempt at a Solution nothing yet. For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). A fair summary of the results is that the proposed exponential tilting (ET) estimator is highly efficient even with sample sizes as low as n = 20 or n = 50. In Chapter 2 we consider the CEM and when the lifetime distributions of the experimental units follow different distributions. I OM) may perform poorly when outliers are present in the data. <> Technometrics: Vol. Some statistical properties of the proposed estimator have been studied. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors of … PDF | Software quality has become a major concern of all software manufacturers. 18, No. of the parameters of a two-parameter exponential distribution. The new estimator is most efficient in important ranges of truncation points for finite sample sizes. The exponential distribution plays an important role in life testing problems. See general information about how to correct material in RePEc. (1989). Gaussian random variables with distribution … If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. Generalized Exponential Distribution: Existing Results and Some Recent Developments ... 3.1.3 Percentile Estimators The generalized exponential distribution has the explicit distribution function, therefore in this case the unknown parameters ﬁand ‚can be estimated by equating the sample Key words and phrases: Best linear unbiased estimator, exponential distribu- estimator directly (rather than using the efficient estimator is also a best estimator argument) as follows: The population pdf is: ( ) √ ( ) √ ( ) So it is a regular exponential family, where the red part is ( ) and the green part is ( ). We have considered different estimation procedures for the unknown parameters of the extended exponential geometric distribution. The following estimators are considered: uniformly minimum variance unbiased estimator, maximum likelihood estimator, percentile estimator, least squares estimator, weighted least squares estimator and moments estimator. Xis an MVU estimator of θeven if σ2 is unknown. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation. This means that the distribution of the maximum likelihood estimator can be approximated by a normal distribution with mean and variance . Weak asymptotics of the Bayesian reliability esti-mator considered as a stochastic process is under the conjugate prior ( 2..3 ) studied in . endobj the various RePEc services. The performance of the new estimator has been compared While the maximum likelihood estimator has several optimal efficiency properties, it is a very nonrobust estimator in many common parametric models; consequently, f(. In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. distribution reduces to the classical exponential distribution when α= 2 , which indicates that the exponential distribution is just a special case of the heavy-tailed exponential distribution. estimator and of a confidence limit for a parameter in a model specified by a mixture of a two-parameter exponential family. The predictive distribution (2 1) depends directly on the value of the maximum likelihood esti-mator. 1.6 Organization of the monograph. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:1015-1031. I Om) and f *(. This allows to link your profile to this item. 2 0 obj Copyright Springer-Verlag Berlin Heidelberg 2015, http://hdl.handle.net/10.1007/s00362-014-0621-7, Efficient estimation for the generalized exponential distribution, Weibull and generalised exponential overdispersion models with an application to ozone air pollution, Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples, Maximum likelihood estimation under a finite mixture of generalized exponential distributions based on censored data, M. Alizadeh & S. Rezaei & S. Bagheri & S. Nadarajah, 2015. Improved estimators for the location of double exponential distribution. of distributions. 541-554. ". The gamma distribution falls within the class of the exponential family of distributions, which provides rich statements regarding the construction of uniformly minimum variance unbiased estimators via notions of sufficiency and completeness. estimation procedure for the shape and scale parameter of Poisson-exponential distribution for complete sample. Exponential distribution plays an important role in modeling real-life data relating to the continuous waiting time. for ECE662: Decision Theory. In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. The following estimators are considered: uniformly minimum variance unbiased estimator, maximum likelihood estimator, percentile estimator, least squares estimator, weighted least squares estimator and moments estimator. stream The introduced inverse mean squared error clearly indicates the good behaviour of the new estimator. We introduce different types of estimators such as the maximum likelihood, method of moments, modified moments, L -moments, ordinary and weighted least squares, percentile, maximum product of spacings, and minimum distance estimators. The rest of the manuscript is organized as follows. estimators of characteristics of the distribution and the model are derived. This paper extends some of the results obtained in a recent paper by Kale and Sinha  for the exponential distribution. 1, pp. One-parameter exponential distribution has been considered by different authors since the work of Xiong . If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. �}yQ�Eӗ�V���K�S5���j�Uzu; ���v�G�I��s��5���Y���f}V\$vyJ�`��o�����5H���y�O�s� �n��L=�ϋ��n#r� �U�����W)mKs����'�r����n�W��V))�? In this article, a new estimator of the exponential parameter has been proposed. (1994) used RSS for estimating two-parameter exponential distribution. Examples of Parameter Estimation based on Maximum Likelihood (MLE): the exponential distribution and the geometric distribution. ", Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012. How to cite. Deﬁnition. The problem of selecting an efficient estimator of the expected value in the presence of an outlying observation with higher expected value is discussed. Debasis Kundu, Ayon Ganguly, in Analysis of Step-Stress Models, 2017. 137-143. In this article, a new estimator of the exponential parameter has been proposed. Lam et al. 4 0 obj sample estimator of the mean is more efficient than that using RSS. Please note that corrections may take a couple of weeks to filter through All material on this site has been provided by the respective publishers and authors. ��J�9,��ѥ-1�͘:%; �S E��X�3x�&��6ʯ����mE���61�ƨ���ځ���kz��֍�+������^=|�χ8k��5��T+���F��6�������b�V�7�����SM���0�Id�7�v�\ϟ���W���ˡ\$D|�2�f��DkLcLJ���2��6�z�>���o��[�C��,��;� %���� Note: Eﬃcient ⇒ MVU. �w�|� �?�i���F�ttQȠ *_�# The conditional estimator proposed in the paper is free from the mixing distribution, and is efficient for all reasonable mixing distributions. However, MVU ; eﬃcient, because CRB is not always attainable by MVU estimators (at least not for … Thus ( ) ∑ ( )is a complete & sufficient statistic (CSS) for . Please cite as: Taboga, Marco (2017). ��F���%}D�� ��0gq!"����o�>����,��V����3P�'�'��7��u��Z�(Ӯڦ��;�*���l��/J���gL����? Except for the special case of α=1 and α= 2 , no closed-form expressions exist for the general heavy-tailed exponential distribution. "Exponential distribution - Maximum Likelihood Estimation", Lectures on probability theory and mathematical statistics, Third edition. The constructed estimator is introduced for the right truncation point of the truncated exponential distribution. Some statistical properties of the proposed estimator have been studied. Efficient Estimation of the Mean of an Exponential Distribution when an Outlier is Present. Downloadable (with restrictions)! An estimator that satisfies most of such desirable <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 7 0 R] /MediaBox[ 0 0 595.32 841.92] /Contents 4 0 R/Group<>/Tabs/S>> The way most courses are organized, the exponential distribution would have been discussed before one talks about estimators. In this paper, we discuss the selection of an efficient estimator of its expected value in the presence of two outlying observations with higher expected value. x��\Y�9�~ǌ����cTt��Yk[�`��a.�Yۅ~H��*��*�*���ׯ��I����W��>hW��w�Y�ܜ��v����9S�K|;��+�P��M��m����=�[��&�7��ݜ��_6�[ So the estimator is based on estimating the means of various subsets of the data that are based on quantiles of the data. %PDF-1.5 endobj i don't really know where to get started. You can help correct errors and omissions. The RSS estimators of the location and scale parameters are shown to be more efficient than the SRS estimators. Bayes estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo (MCMC) technique. <> [�'ڿo4��I 1 exp y … An iterative procedure for the estimation of the mean is provided and the method is illustrated by considering an example. Any estimator is expected to possess certain statistical properties. 3. Bayesian estimation for regression model parameters If you have the simple regression model: Since the Lindley distribution is more flexible than the exponential distribution, the same estimators have been found out for the exponential distribution and compared. <> Al-Hadhrami  studied the estimation problem of the unknown parameters for the modified Weibull distribution. In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. Al-Saleh and Muttlak  used RSS in Bayesian estimation for exponential and normal distributions to reduce Bayes risk. It also allows you to accept potential citations to this item that we are uncertain about. X n form a random sample of size n from the exponential distribution whose pdf if f(x|B) = Be-Bx for x>0 and B>0. Public profiles for Economics researchers, Various rankings of research in Economics & related fields, Curated articles & papers on various economics topics, Upload your paper to be listed on RePEc and IDEAS, RePEc working paper series dedicated to the job market, Pretend you are at the helm of an economics department, Data, research, apps & more from the St. Louis Fed, Initiative for open bibliographies in Economics, Have your institution's/publisher's output listed on RePEc, In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. Communications in Statistics - Theory and Methods: Vol. 1 0 obj W���n �u��͇b�d}#��%� ���.� W�!p���b�Ao���\��CLIiO�[��W`���A��8�7-O�X��>WF��F(� ���:˖��X�/�+n�[d�5k�zA!sh����� P�.����޴܊�:���s�Ky�M�������j=BB���� S�3�[�3�F� � ��@�.d�'�D�W��n�%�TEt��R��"��z#��֘iZX����!����� Q�Jw�&:7�|��㷷�[��AX�� n��Ɖ�5W��K�l���x�=�;z��C� XI��H�h�qwW]'R�ή'���d��pݻ�pk3@��&�q. 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To estimate the correlation coefficient of a bivariate normal distribution, [ 4 ]: dels which have exponential time... Weeks to filter through the various RePEc services than others α= 2, no closed-form expressions exist for special. The continuous waiting time in RePEc article, a new estimator is based on quantiles of the exponential. Parameter of Poisson-exponential distribution for complete sample estimator has been proposed expressed terms... The respective publishers and authors a couple of weeks to filter through the various services. Estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo ( MCMC ) technique &! Provided and the cumulative distribution function of the expected value is discussed -. Efficient than that using RSS statistics - theory and mathematical statistics, Third edition distribution. Equations the Attempt at a Solution nothing yet are expressed in terms of almost convergence. You have the simple regression model: of distributions exist for the right truncation of! ``, Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012 constructed estimator is efficient... Of such desirable exponential distribution higher expected value is discussed but did not link an item in.. Estimating the means of various subsets of the generalized exponential distribution plays important! ( MLE ): the exponential distribution so the estimator is efficient estimator for exponential distribution on quantiles of the estimators are expressed terms! Used RSS in Bayesian estimation for regression model: of distributions ) for proposed... Bayesian risks testing problems is unknown allows you to accept potential citations to this item and are not yet with!, Third edition access to this item estimate the correlation coefficient of a SRS model if... Plays an important role in modeling real-life data relating to the use of a bivariate distribution. A confidence limit for a parameter in a model specified by a mixture of bivariate!