Efficient Estimation of the Mean of an Exponential Distribution when an Outlier is Present. Exponential distribution plays an important role in modeling real-life data relating to the continuous waiting time. If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form . $\endgroup$ – André Nicolas Mar 11 '14 at 1:06 | … Key words and phrases: Best linear unbiased estimator, exponential distribu- However, MVU ; efficient, because CRB is not always attainable by MVU estimators (at least not for … ". "Exponential distribution - Maximum Likelihood Estimation", Lectures on probability theory and mathematical statistics, Third edition. All material on this site has been provided by the respective publishers and authors. iii. The problem of selecting an efficient estimator of the expected value in the presence of an outlying observation with higher expected value is discussed. So the estimator is based on estimating the means of various subsets of the data that are based on quantiles of the data. Improved estimators for the location of double exponential distribution. It also allows you to accept potential citations to this item that we are uncertain about. 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. 1.6 Organization of the monograph. 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$D|�2�f��DkLcLJ���2��6�z�>���o��[�C��,��;� Complement to Lecture 7: "Comparison of Maximum likelihood (MLE) and Bayesian Parameter Estimation" We introduce different types of estimators such as the maximum likelihood, method of moments, modified moments, L -moments, ordinary and weighted least squares, percentile, maximum product of spacings, and minimum distance estimators. This allows to link your profile to this item. The conditional estimator proposed in the paper is free from the mixing distribution, and is efficient for all reasonable mixing distributions. <> distribution reduces to the classical exponential distribution when α= 2 , which indicates that the exponential distribution is just a special case of the heavy-tailed exponential distribution. ?����J��� g�G� N9Z����Hk��u 3 0 obj Analytical expressions are derived for the bias and the mean squared error. �}yQ�Eӗ�V���K�S5���j�Uzu; ���v�G�I��s��5���Y���f}V$vyJ�`��o�����5H���y�O�s� �n��L=�ϋ��n#r� �U�����W)mKs����'�r����n�W��V))�? Please note that corrections may take a couple of weeks to filter through Examples of Parameter Estimation based on Maximum Likelihood (MLE): the exponential distribution and the geometric distribution. One-parameter exponential distribution has been considered by different authors since the work of Xiong [29]. Except for the special case of α=1 and α= 2 , no closed-form expressions exist for the general heavy-tailed exponential distribution. Bayesian estimation for regression model parameters If you have the simple regression model: The new estimator is most efficient in important ranges of truncation points for finite sample sizes. Al-Hadhrami [8] studied the estimation problem of the unknown parameters for the modified Weibull 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). %���� You can help correct errors and omissions. endobj 3. endobj Lam et al. 14, No. (1994) used RSS for estimating two-parameter exponential distribution. 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. 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 Furthermore, it maintains the high efficiency even for the heavy-tailed t 3 error distribution. (1972). 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 … [�'ڿo4��I 4 0 obj i don't really know where to get started. 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. 2, pp. a push in … estimation procedure for the shape and scale parameter of Poisson-exponential distribution for complete sample. endobj It turns out that the use of RSS and its suitable modifications results in much improved estimators compared to the use of a SRS. <>/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>> An iterative procedure for the estimation of the mean is provided and the method is illustrated by considering an example. 18, No. stream for ECE662: Decision Theory. <> This means that the distribution of the maximum likelihood estimator can be approximated by a normal distribution with mean and variance . An unbiased estimator of θthat attains the CRB for θfor all θin the parameter space Θ is said to be efficient. I Om) and f *(. This paper extends some of the results obtained in a recent paper by Kale and Sinha [3] for the exponential distribution. 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 this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. Simulation studies and real data applications show that the maximum likelihood estimator performs better than others. 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. Some statistical properties of the proposed estimator have been studied. I OM) may perform poorly when outliers are present in the data. While the maximum likelihood estimator has several optimal efficiency properties, it is a very nonrobust estimator in many common parametric models; consequently, f(. Homework Equations The Attempt at a Solution nothing yet. Technometrics: Vol. Definition. of distributions. General contact details of provider: http://www.springer.com . Weak asymptotics of the Bayesian reliability esti-mator considered as a stochastic process is under the conjugate prior ( 2..3 ) studied in [4]. Exponential class software reliability models [2], [4]: dels which have exponential failure time distribution. The exponential distribution plays an important role in life testing problems. 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. If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. 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. Some statistical properties of the proposed estimator have been studied. 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. estimators of characteristics of the distribution and the model are derived. In this article, a new estimator of the exponential parameter has been proposed. Since the Lindley distribution is more flexible than the exponential distribution, the same estimators have been found out for the exponential distribution and compared. 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 . Thus ( ) ∑ ( )is a complete & sufficient statistic (CSS) for . I rewrote the computations as SAS/IML functions to make them more efficient … 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. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:1015-1031. The RSS estimators of the location and scale parameters are shown to be more efficient than the SRS estimators. 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. Problem of selecting an efficient estimator of θeven if σ2 is unknown are based on quantiles of new... 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