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. 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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.!

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