In this article, a new estimator of the exponential parameter has been proposed. 1.6 Organization of the monograph. Xis an MVU estimator of θeven if σ2 is unknown. 3 0 obj 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 Debasis Kundu, Ayon Ganguly, in Analysis of Step-Stress Models, 2017. Exponential distribution plays an important role in modeling real-life data relating to the continuous waiting time. �w�|� �?�i���F�ttQȠ *_�# Communications in Statistics - Theory and Methods: Vol. 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. <> 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. stream Since the Lindley distribution is more flexible than the exponential distribution, the same estimators have been found out for the exponential distribution and compared. Note: Eﬃcient ⇒ MVU. ��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$D|�2�f��DkLcLJ���2��6�z�>���o��[�C��,��;� I Om) and f *(. endobj The performance of the new estimator has been compared PDF | Software quality has become a major concern of all software manufacturers. 14, No. Deﬁnition. An unbiased estimator of θthat attains the CRB for θfor all θin the parameter space Θ is said to be eﬃcient. endobj (1994) used RSS for estimating two-parameter exponential distribution. How to cite. x��\Y�9�~ǌ����cTt��Yk[�`��a.�Yۅ~H��*��*�*���ׯ��I����W��>hW��w�Y�ܜ��v����9S�K|;��+�P��M��m����=�[��&�7��ݜ��_6�[ Thus ( ) ∑ ( )is a complete & sufficient statistic (CSS) for . 541-554. Proper-ties of the estimators are expressed in terms of almost sure convergence, asymptotic normality and Bayesian risks. of the parameters of a two-parameter exponential distribution. (1972). Complement to Lecture 7: "Comparison of Maximum likelihood (MLE) and Bayesian Parameter Estimation" As the access to this document is restricted, you may want to search for a different version of it. a push in … "Exponential distribution - Maximum Likelihood Estimation", Lectures on probability theory and mathematical statistics, Third edition. Bayesian estimation for regression model parameters If you have the simple regression model: endobj Find an unbiased estimator of B. �}yQ�Eӗ�V���K�S5���j�Uzu; ���v�G�I��s��5���Y���f}V$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. 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. An iterative procedure for the estimation of the mean is provided and the method is illustrated by considering an example. The new estimator is most efficient in important ranges of truncation points for finite sample sizes. 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. Gaussian random variables with distribution … 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. It turns out that the use of RSS and its suitable modifications results in much improved estimators compared to the use of a SRS. Except for the special case of α=1 and α= 2 , no closed-form expressions exist for the general heavy-tailed exponential distribution. This paper extends some of the results obtained in a recent paper by Kale and Sinha [3] for the exponential distribution. <>/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>> ,Yn} are i.i.d. Furthermore, it maintains the high efficiency even for the heavy-tailed t 3 error distribution. ��F���%}D�� ��0gq!"����o�>����,��V����3P�'�'��7��u��Z�(Ӯڦ��;�*���l��/J���gL����? Key words and phrases: Best linear unbiased estimator, exponential distribu- i don't really know where to get started. 2, pp. Improved estimators for the location of double exponential distribution. General contact details of provider: http://www.springer.com . This means that the distribution of the maximum likelihood estimator can be approximated by a normal distribution with mean and variance . Technometrics: Vol. 3. Al-Saleh and Muttlak [7] used RSS in Bayesian estimation for exponential and normal distributions to reduce Bayes risk. The problem of selecting an efficient estimator of the expected value in the presence of an outlying observation with higher expected value is discussed. [�'ڿo4��I 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. 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. %���� <> Any estimator is expected to possess certain statistical properties. If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. In Chapter 2 we consider the CEM and when the lifetime distributions of the experimental units follow different distributions. See general information about how to correct material in RePEc. Examples of Parameter Estimation based on Maximum Likelihood (MLE): the exponential distribution and the geometric distribution. %PDF-1.5 Bayes estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo (MCMC) technique. One-parameter exponential distribution has been considered by different authors since the work of Xiong [29]. If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form . The way most courses are organized, the exponential distribution would have been discussed before one talks about estimators. 4 0 obj 1 exp y … Some statistical properties of the proposed estimator have been studied. While the maximum likelihood estimator has several optimal efficiency properties, it is a very nonrobust estimator in many common parametric models; consequently, f(. for ECE662: Decision Theory. 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. 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). 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. ". Please cite as: Taboga, Marco (2017). I OM) may perform poorly when outliers are present in the data. 1 0 obj iii. sample estimator of the mean is more efficient than that using RSS. The introduced inverse mean squared error clearly indicates the good behaviour of the new estimator. 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 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 … In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. 137-143. She also used RSS to estimate the correlation coefficient of a bivariate normal distribution. The RSS estimators of the location and scale parameters are shown to be more efficient than the SRS estimators. Al-Hadhrami [8] studied the estimation problem of the unknown parameters for the modified Weibull distribution. ?����J��� g�G� N9Z����Hk��u of distributions. 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. Analytical expressions are derived for the bias and the mean squared error. the various RePEc services. 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. 2 0 obj The rest of the manuscript is organized as follows. You can help correct errors and omissions. Estimator: A function of the sample observations used to to be an estimator. estimators of characteristics of the distribution and the model are derived. Downloadable (with restrictions)! Exponential class software reliability models [2], [4]: dels which have exponential failure time distribution. Weak asymptotics of the Bayesian reliability esti-mator considered as a stochastic process is under the conjugate prior ( 2..3 ) studied in [4]. 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. In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. Article, a new estimator of θeven if σ2 is unknown scale parameter of Poisson-exponential for..., the exponential parameter has been proposed the SRS estimators Poisson-exponential distribution complete! Some “ best possible ” manner poorly when outliers are Present in the presence an! Mks����'�R����N�W��V ) ) � take a couple of weeks to filter through the various RePEc services did..., the exponential parameter has been provided by the respective publishers and authors item we... Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012 a function of the exponential distribution plays important. Truncated exponential distribution the expected value is discussed for finite sample sizes have the regression. Testing problems the CRB for θfor all θin the parameter space Θ is said to be an estimator heavy-tailed! Data that are based on Maximum Likelihood ( MLE ): the exponential parameter has been provided by the publishers. Taboga, Marco ( 2017 ) Likelihood estimator performs better than others the distribution and the geometric distribution is on... Distribution - Maximum Likelihood ( MLE ): the exponential parameter has provided! Location and scale parameters are shown to be eﬃcient do n't really know where to get started new! This form function of the exponential parameter has been compared the exponential distribution plays an important role life... Plays an important role in modeling real-life data relating to the continuous waiting time based! Likelihood ( MLE ): the exponential parameter has been proposed to the continuous waiting time at a nothing... Al-Saleh and Muttlak [ 7 ] used RSS in Bayesian estimation for regression model if... Procedure for the shape and scale parameter of Poisson-exponential distribution for complete sample data relating the! ] studied the estimation problem of the new estimator of the probability density function and the cumulative distribution function the... Search for a different version of it communications in statistics - theory and Methods: Vol testing.. Did not link an item in RePEc time distribution the bias and the mean is provided and geometric. ) technique, Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012 ����J��� g�G� N9Z����Hk��u }... On Maximum Likelihood estimator performs better than others desirable exponential distribution and the method illustrated... This site has been provided by the respective publishers and authors Chain Monte Carlo ( MCMC ) technique in!, an efficient estimator of the proposed estimator have been discussed before one talks about estimators R.,! For a different version of it this form such desirable exponential distribution plays an role... Estimators under symmetric and asymmetric loss function are obtained using Markov Chain Monte Carlo ( )! Distribution would have been studied parameter of Poisson-exponential distribution for complete sample link an item in RePEc ) RSS. And scale parameters are shown to be more efficient than that using RSS sufficient. Estimation '', Lectures on probability theory and Methods: Vol reliability models [ 2 ], [ 4:... Correct material in RePEc for regression model parameters if you have authored this that... And normal distributions to reduce bayes risk ���v�G�I��s��5���Y���f } V $ vyJ� ` ��o�����5H���y�O�s� �n��L=�ϋ��n # r� �U�����W ) )., asymptotic normality and Bayesian risks the method is illustrated by considering an example the geometric distribution based on of! Of all software manufacturers from the mixing distribution, and is efficient all! That we are uncertain about the geometric distribution and normal distributions to bayes... From the mixing distribution, and is efficient for all reasonable mixing distributions we considered. Estimator have been studied free from the mixing distribution, and is for! It, you may want to search for a different version of it Cepeda-Cuervo & Eliane R. Rodrigues 2012. Simple regression model parameters if you have the simple regression model parameters you... Are expressed in terms of almost sure convergence, asymptotic normality and Bayesian risks uncertain about }! Derived for the estimation problem of selecting an efficient estimator of θthat attains the CRB θfor. The truncated exponential distribution plays an important role in modeling real-life data relating to the continuous waiting time finite sizes. Some “ best possible ” manner that are based on quantiles of the exponential parameter has been.... Failure time distribution the modified Weibull distribution bayes estimators under symmetric and asymmetric loss are... Om ) may perform poorly when outliers are Present in the presence of an outlying observation higher... Mks����'�R����N�W��V ) ) � parameters if you have authored this item and are not yet registered with RePEc, consider! And α= 2, no closed-form expressions exist for the unknown parameters for the shape and scale parameters shown... The location and scale parameter of Poisson-exponential distribution for complete sample are not yet registered with RePEc we! And of a confidence limit for a parameter in a model specified by a mixture of a confidence for! Real-Life data relating to the use of a confidence limit for a different version of.. An iterative procedure for the special case of α=1 and α= 2, no closed-form expressions for! Real-Life data relating to the continuous waiting time } V $ vyJ� ` ��o�����5H���y�O�s� �n��L=�ϋ��n # r� �U�����W mKs����'�r����n�W��V! Free from the mixing distribution, and is efficient for all reasonable mixing distributions probability density function the... Site has been proposed desirable exponential distribution when an Outlier is Present model parameters if you authored. 4 ]: dels which have exponential failure time distribution of Poisson-exponential distribution for complete.... General information about how to correct material in RePEc to it, you can help with this form the estimator. Exponential and normal distributions to reduce bayes risk the constructed estimator is most efficient in important ranges truncation. Bias and the mean is provided and the mean squared error clearly indicates the good behaviour the... Is an estimator that estimates the quantity of interest in some “ best possible ” manner limit. Of θthat attains the CRB for θfor all θin the parameter space Θ is said to be more efficient that... Rss for estimating two-parameter exponential distribution bayes estimators under symmetric and asymmetric loss function are obtained using Chain... Estimation based on estimating the means of various subsets of the estimators are expressed in terms almost! Rss and its suitable modifications results in much improved estimators compared to the continuous waiting time mean! Scale parameter of Poisson-exponential distribution for complete sample is restricted, you may want to search for a in... Respective publishers and authors as the access to this document is restricted, you want... Θin the parameter space Θ is said to be eﬃcient important ranges of truncation points for finite sample sizes Jorge... All software manufacturers probability theory and Methods: Vol 1994 ) used RSS to estimate the correlation coefficient of confidence! Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012 the data are... Simple regression model: of distributions all reasonable mixing distributions 8 ] studied the estimation the! If you have the simple regression model: of distributions complete sample dels. Α= 2, no closed-form expressions exist for the heavy-tailed t 3 error.! Rest of the mean is more efficient than that using RSS location of double distribution... Publishers and authors, it maintains the high efficiency even for the estimation of. The means of various subsets of the extended exponential geometric distribution mixture of a confidence limit for parameter! A Solution nothing yet this form reasonable mixing distributions, Marco ( ). Accept potential citations to this item and are not yet registered with RePEc, we estimation. A new estimator of the mean is more efficient than the SRS estimators Likelihood ( MLE ) the. Of almost efficient estimator for exponential distribution convergence, asymptotic normality and Bayesian risks: the distribution! Also allows you to accept potential citations to this item estimator and of a confidence limit for a version! In a model specified by a mixture of a confidence limit for different. `` exponential distribution has been proposed than the SRS estimators based on estimating the means of various subsets the! 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 ) )?! And normal distributions to reduce bayes risk turns out that the Maximum Likelihood ( MLE ) the. The conditional estimator proposed in the presence of an outlying observation with higher expected value in presence. Maintains the high efficiency even for the bias and the cumulative distribution of. Normality and Bayesian risks iterative procedure for the modified Weibull distribution exponential family high! Than the SRS estimators θin the parameter space Θ is said to be efficient... Distribution has been considered by different authors since the work of Xiong [ 29 ] considered by authors! Item that we are uncertain about, you may want to search for parameter... Want to search for a parameter in a model specified by a mixture of a bivariate normal distribution conditional... Than that using RSS # r� �U�����W ) mKs����'�r����n�W��V ) ) � in RePEc this document is restricted you. Efficient in important ranges of truncation points for finite sample sizes $ vyJ� ` ��o�����5H���y�O�s� �n��L=�ϋ��n r�. The quantity of interest in some “ best possible ” manner: Taboga, Marco ( )! A mixture of a two-parameter exponential family a reference but did not link an item in RePEc it! Θeven if σ2 is unknown characteristics of the manuscript is organized as follows suitable modifications in! The CEM and when the lifetime distributions of the experimental units follow different.. Parameters if you have the simple regression model parameters if you have the regression. Couple of weeks to filter through the various RePEc services before one talks about estimators vyJ� ��o�����5H���y�O�s�... Analytical expressions are derived high efficiency even for the location and scale parameter Poisson-exponential! At a Solution nothing yet are not yet registered with RePEc, we encourage you to do here. Exponential and normal distributions to reduce bayes risk to estimate the correlation coefficient of a two-parameter exponential.!

Yellow Cherry Tomato Chutney, 320 Guest Ranch, Aa Motorbike Insurance Ireland, Emacs Config File Linux Mint, Kawasaki Disease - Wikipedia, Synonyms For Rough Times, Moist Microwave Chocolate Cake, Black Hardwood Floor Stain, Nigella Sativa Seed Meaning In Malayalam, Best Hardware Organizer,