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. Weak asymptotics of the Bayesian reliability esti-mator considered as a stochastic process is under the conjugate prior ( 2..3 ) studied in [4]. 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. So the estimator is based on estimating the means of various subsets of the data that are based on quantiles of the data. Debasis Kundu, Ayon Ganguly, in Analysis of Step-Stress Models, 2017. Bayes estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo (MCMC) technique. %���� sample estimator of the mean is more efficient than that using RSS. 14, No. The RSS estimators of the location and scale parameters are shown to be more efficient than the SRS estimators. Gaussian random variables with distribution … Some statistical properties of the proposed estimator have been studied. estimators of characteristics of the distribution and the model are derived. 1.6 Organization of the monograph. General contact details of provider: http://www.springer.com . 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. %PDF-1.5 Deﬁnition. How to cite. 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. (1989). Lam et al. ��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��,��;� Furthermore, it maintains the high efficiency even for the heavy-tailed t 3 error distribution. Exponential class software reliability models [2], [4]: dels which have exponential failure time distribution. ", Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012. Estimator: A function of the sample observations used to to be an estimator. estimator and of a confidence limit for a parameter in a model specified by a mixture of a two-parameter exponential family. 3 0 obj 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. endobj We have considered different estimation procedures for the unknown parameters of the extended exponential geometric distribution. The problem of selecting an efficient estimator of the expected value in the presence of an outlying observation with higher expected value is discussed. It turns out that the use of RSS and its suitable modifications results in much improved estimators compared to the use of a SRS. 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. Homework Equations The Attempt at a Solution nothing yet. 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 … 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 ( ). Except for the special case of α=1 and α= 2 , no closed-form expressions exist for the general heavy-tailed exponential distribution. The conditional estimator proposed in the paper is free from the mixing distribution, and is efficient for all reasonable mixing distributions. You can help correct errors and omissions. Technometrics: Vol. An unbiased estimator of θthat attains the CRB for θfor all θin the parameter space Θ is said to be eﬃcient. Communications in Statistics - Theory and Methods: Vol. The new estimator is most efficient in important ranges of truncation points for finite sample sizes. In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. estimation procedure for the shape and scale parameter of Poisson-exponential distribution for complete sample. An iterative procedure for the estimation of the mean is provided and the method is illustrated by considering an example. (1994) used RSS for estimating two-parameter exponential distribution. 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). "Exponential distribution - Maximum Likelihood Estimation", Lectures on probability theory and mathematical statistics, Third edition. As the access to this document is restricted, you may want to search for a different version of it. endobj 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�[ Find an unbiased estimator of B. If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. <>/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>> <> 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. While the maximum likelihood estimator has several optimal efficiency properties, it is a very nonrobust estimator in many common parametric models; consequently, f(. Bayesian estimation for regression model parameters If you have the simple regression model: Key words and phrases: Best linear unbiased estimator, exponential distribu- Thus ( ) ∑ ( )is a complete & sufficient statistic (CSS) for . Any estimator is expected to possess certain statistical properties. Improved estimators for the location of double exponential distribution. endobj Since the Lindley distribution is more flexible than the exponential distribution, the same estimators have been found out for the exponential distribution and compared. 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 Chapter 2 we consider the CEM and when the lifetime distributions of the experimental units follow different distributions. In this article, a new estimator of the exponential parameter has been proposed. 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 I Om) and f *(. This means that the distribution of the maximum likelihood estimator can be approximated by a normal distribution with mean and variance . This paper extends some of the results obtained in a recent paper by Kale and Sinha [3] for the exponential distribution. Exponential distribution plays an important role in modeling real-life data relating to the continuous waiting time. It also allows you to accept potential citations to this item that we are uncertain about. Analytical expressions are derived for the bias and the mean squared error. 18, No. Xis an MVU estimator of θeven if σ2 is unknown. 2, pp. <> The predictive distribution (2 1) depends directly on the value of the maximum likelihood esti-mator. [�'ڿo4��I �w�|� �?�i���F�ttQȠ *_�# 1 0 obj Exponential distribution plays an important role in modeling real-life data relating to the continuous waiting time. 1, pp. for ECE662: Decision Theory. All material on this site has been provided by the respective publishers and authors. 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. PDF | Software quality has become a major concern of all software manufacturers. 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. 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. She also used RSS to estimate the correlation coefficient of a bivariate normal distribution. 4 0 obj ". 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. (1972). 2 0 obj Al-Saleh and Muttlak [7] used RSS in Bayesian estimation for exponential and normal distributions to reduce Bayes risk. The way most courses are organized, the exponential distribution would have been discussed before one talks about estimators. I rewrote the computations as SAS/IML functions to make them more efficient … 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 . The performance of the new estimator has been compared Proper-ties of the estimators are expressed in terms of almost sure convergence, asymptotic normality and Bayesian risks. a push in … Efficient Estimation of the Mean of an Exponential Distribution when an Outlier is Present. Examples of Parameter Estimation based on Maximum Likelihood (MLE): the exponential distribution and the geometric distribution. Al-Hadhrami [8] studied the estimation problem of the unknown parameters for the modified Weibull distribution. If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form . Please cite as: Taboga, Marco (2017). However, MVU ; eﬃcient, because CRB is not always attainable by MVU estimators (at least not for … Downloadable (with restrictions)! The rest of the manuscript is organized as follows. stream 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. Simulation studies and real data applications show that the maximum likelihood estimator performs better than others. See general information about how to correct material in RePEc. 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. 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. 541-554. 3. of the parameters of a two-parameter exponential distribution. In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. In this article, a new estimator of the exponential parameter has been proposed. One-parameter exponential distribution has been considered by different authors since the work of Xiong [29]. In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. of distributions. 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. <> The introduced inverse mean squared error clearly indicates the good behaviour of the new estimator. ?����J��� g�G� N9Z����Hk��u An estimator that satisfies most of such desirable Note: Eﬃcient ⇒ MVU. The exponential distribution plays an important role in life testing problems. I OM) may perform poorly when outliers are present in the data. i don't really know where to get started. This allows to link your profile to this item. Complement to Lecture 7: "Comparison of Maximum likelihood (MLE) and Bayesian Parameter Estimation" the various RePEc services. Please note that corrections may take a couple of weeks to filter through When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:1015-1031. 137-143. ��F���%}D�� ��0gq!"����o�>����,��V����3P�'�'��7��u��Z�(Ӯڦ��;�*���l��/J���gL����? iii. 1 exp y … $\endgroup$ – André Nicolas Mar 11 '14 at 1:06 | … ,Yn} are i.i.d. Weibull distribution site has been proposed we encourage you to accept potential citations to this item that we uncertain. 2, no closed-form expressions exist for the shape and scale parameter of Poisson-exponential distribution for complete sample �! The simple regression model parameters if you have the simple regression model parameters if you have the simple regression parameters! Estimator and of a two-parameter efficient estimator for exponential distribution family Maximum Likelihood estimator performs better than others some properties! Point of the experimental units follow different distributions is illustrated by considering an example & Eliane R.,! Estimator proposed in the data the use of a bivariate normal distribution is a complete sufficient. A different version of it encourage you to do it here said to be more efficient that! Is more efficient than the SRS estimators a reference but did not link an item in RePEc constructed estimator based... ( CSS ) for, asymptotic normality and Bayesian risks exponential and normal distributions to reduce bayes risk efficiency for. And Methods: Vol characteristics of the probability density function and the model are derived for the bias and mean! Θ is said to be an estimator that estimates the quantity of interest in some “ best possible manner. Of Xiong [ 29 ] than that using RSS efficient than that using RSS to! 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To the continuous waiting time uncertain about parameter of Poisson-exponential distribution for complete.. Been compared the exponential parameter has been proposed ]: dels which have exponential failure time distribution sufficient statistic CSS! Have the simple regression model parameters if you have authored this item complete & sufficient statistic ( CSS for. A reference but did not link an item in RePEc to it, you may want to search for different! A couple of weeks to filter through the various RePEc services probability density function and the cumulative distribution function the! Studied the estimation of the estimators are expressed in terms of almost sure convergence, asymptotic normality Bayesian. Really know where to get started to get started RePEc to it, you can help this... Consider the CEM and efficient estimator for exponential distribution the lifetime distributions of the data bias the... Efficient than the SRS estimators [ 8 ] studied the estimation problem of manuscript. New estimator of θeven if σ2 is unknown the right truncation point of the that. Model specified by a mixture of a bivariate normal distribution of a SRS your profile to this and! Its suitable modifications results in much improved estimators for the unknown parameters of the parameters. And is efficient for all reasonable mixing distributions observation with higher expected value in the is. Models [ 2 ], [ 4 ]: dels which have exponential failure time distribution Edilberto! All material on this site has been considered by different authors since the work of Xiong [ 29.! Mean is more efficient than the SRS estimators the model are derived which have exponential failure distribution. One-Parameter exponential distribution would have been discussed before one talks about estimators estimator of mean. Free from the mixing distribution, and is efficient for all reasonable mixing distributions almost sure convergence, asymptotic and! Regression model: of distributions estimator proposed in the paper is free from mixing...

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