Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation
In this paper we discuss the behavlor of the statistic R^(t) , the uniformly minimum variance unbiased (UMVU) estimate for the reliability of gamma distribution with unknown scale parameter σ when an outlier observation is present. Given the outlier effect on σ, we determine bounds for the mean and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000980 |
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| author | M. E. Ghitany W. H. Laverty |
| author_facet | M. E. Ghitany W. H. Laverty |
| author_sort | M. E. Ghitany |
| collection | DOAJ |
| description | In this paper we discuss the behavlor of the statistic R^(t)
, the uniformly
minimum variance unbiased (UMVU) estimate for the reliability of gamma distribution
with unknown scale parameter σ when an outlier observation is present. Given the
outlier effect on σ, we determine bounds for the mean and mean square error (MSE) of
R(t). A semi-Bayesian approach is discussed when the outlier effect on σ
is treated
as a random variable having a prior distribution of beta type. Results of the
exponential distribution (Sinha [1]) are given as particular cases of our results. |
| format | Article |
| id | doaj-art-f5fcdf74582d42498b9f765138d8af93 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f5fcdf74582d42498b9f765138d8af932025-02-03T06:11:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112479780410.1155/S0161171289000980Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observationM. E. Ghitany0W. H. Laverty1Department of Mathematics, University of Saskatchewan, Saskatoon S7N OWO, Saskatchewan, CanadaDepartment of Mathematics, University of Saskatchewan, Saskatoon S7N OWO, Saskatchewan, CanadaIn this paper we discuss the behavlor of the statistic R^(t) , the uniformly minimum variance unbiased (UMVU) estimate for the reliability of gamma distribution with unknown scale parameter σ when an outlier observation is present. Given the outlier effect on σ, we determine bounds for the mean and mean square error (MSE) of R(t). A semi-Bayesian approach is discussed when the outlier effect on σ is treated as a random variable having a prior distribution of beta type. Results of the exponential distribution (Sinha [1]) are given as particular cases of our results.http://dx.doi.org/10.1155/S0161171289000980 |
| spellingShingle | M. E. Ghitany W. H. Laverty Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation International Journal of Mathematics and Mathematical Sciences |
| title | Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation |
| title_full | Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation |
| title_fullStr | Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation |
| title_full_unstemmed | Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation |
| title_short | Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation |
| title_sort | bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation |
| url | http://dx.doi.org/10.1155/S0161171289000980 |
| work_keys_str_mv | AT meghitany boundsforthemeansquareerrorofreliabilityestimationfromgammadistributioninpresenceofanoutlierobservation AT whlaverty boundsforthemeansquareerrorofreliabilityestimationfromgammadistributioninpresenceofanoutlierobservation |