efficient estimator for exponential distribution

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