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Details van artikel 31 van 82 gevonden artikelen
| Titel: |
Efficient Estimation of Normal Population Mean |
| Auteur: |
Ashok Sahai M. Raghunadh Acharya Hydar Ali |
| Verschenen in: |
Journal of applied sciences |
| Paginering: | Jaargang 6 (2006) nr. 9 pagina's 1966-1968 |
| Jaar: |
2006 |
| Inhoud: |
In 1964, Searls provided the Minimum Mean Squared Error (MMSE) estimator (1 + σ2/nμ2)-1 <img src="../xml/jas/2006/image1-2k6-1966-1968.gif" width="17" height="15"> in the class of estimators of the type <img src="../xml/jas/2006/image2-2k6-1966-1968.gif" width="17" height="15"> for estimating the mean μ of a normal population with variance σ2. However, as (σ/μ) is seldom known, this MMSE estimator is not very useful, in practice. In 1980, Srivastava, therefore, proposed the correspondingly computable estimator t = <img src="../xml/jas/2006/image1-2k6-1966-1968.gif" width="17" height="15">/(1 + s2/(n<img src="../xml/jas/2006/image4-2k6-1966-1968.gif" width="17" height="15">)) and showed that it is more efficient than the usual estimator <img src="../xml/jas/2006/image1-2k6-1966-1968.gif" width="17" height="15"> whenever σ2/(μσ2) is at least 0.5. Nevertheless, the relevant gain in efficiency would be still unknown as it involves the unknown population parameters μ and σ2. In 1990, Srivastava and Singh provided an UMVU estimate of the Relative Efficiency ratio, E(<<img src="../xml/jas/2006/image3-2k6-1966-1968.gif" width="30" height="16"> )2/E(t - μ)2 to help determine the usefulness of the estimator t over the usual sample mean estimator <img src="../xml/jas/2006/image1-2k6-1966-1968.gif" width="17" height="15"> in practice. In most cases the coefficient of variation of the sample mean estimator , which is more stable than the original variable X and hence, its sample counterpart, could be rather low. For such situations, the present study proposes tø = <img src="../xml/jas/2006/image1-2k6-1966-1968.gif" width="17" height="15">(1 + s2/(n<img src="../xml/jas/2006/image4-2k6-1966-1968.gif" width="17" height="15">)) and studies it on the lines similar to those of the estimator t of Srivastava and Singh. The motivating objective, to improve t in practical situations is amply achieved. |
| Uitgever: |
Asian Network for Scientific Information (provided by DOAJ) |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 31 van 82 gevonden artikelen
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