A New Lifetime Distribution and Its Power Transformation
New one-parameter and two-parameter distributions are introduced in this paper. The failure rate of the one-parameter distribution is unimodal (upside-down bathtub), while the failure rate of the two-parameter distribution can be decreasing, increasing, unimodal, increasing-decreasing-increasing, or...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2014/532024 |
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| _version_ | 1832555955268616192 |
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| author | Ammar M. Sarhan Lotfi Tadj David C. Hamilton |
| author_facet | Ammar M. Sarhan Lotfi Tadj David C. Hamilton |
| author_sort | Ammar M. Sarhan |
| collection | DOAJ |
| description | New one-parameter and two-parameter distributions are introduced in this paper. The failure rate of the one-parameter distribution is unimodal (upside-down bathtub), while the failure rate of the two-parameter distribution can be decreasing, increasing, unimodal, increasing-decreasing-increasing, or decreasing-increasing-decreasing, depending on the values of its two parameters. The two-parameter distribution is derived from the one-parameter distribution by using a power transformation. We discuss some properties of these two distributions, such as the behavior of the failure rate function, the probability density function, the moments, skewness, and kurtosis, and limiting distributions of order statistics. Maximum likelihood estimation for the two-parameter model using complete samples is investigated. Different algorithms for generating random samples from the two new models are given. Applications to real data are discussed and compared with the fit attained by some one- and two-parameter distributions. Finally, a simulation study is carried out to investigate the mean square error of the maximum likelihood estimators, the coverage probability, and the width of the confidence intervals of the unknown parameters. |
| format | Article |
| id | doaj-art-c6377cc9608046a59de75c7db34aa0bf |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-c6377cc9608046a59de75c7db34aa0bf2025-02-03T05:46:51ZengWileyJournal of Probability and Statistics1687-952X1687-95382014-01-01201410.1155/2014/532024532024A New Lifetime Distribution and Its Power TransformationAmmar M. Sarhan0Lotfi Tadj1David C. Hamilton2Department of Mathematics, Dalhousie University, Halifax, NS, B3H 4R2, CanadaDepartment of Information Systems and Decision Sciences, Fairleigh Dickinson University, Vancouver, BC, V6B 2P6, CanadaDepartment of Mathematics, Dalhousie University, Halifax, NS, B3H 4R2, CanadaNew one-parameter and two-parameter distributions are introduced in this paper. The failure rate of the one-parameter distribution is unimodal (upside-down bathtub), while the failure rate of the two-parameter distribution can be decreasing, increasing, unimodal, increasing-decreasing-increasing, or decreasing-increasing-decreasing, depending on the values of its two parameters. The two-parameter distribution is derived from the one-parameter distribution by using a power transformation. We discuss some properties of these two distributions, such as the behavior of the failure rate function, the probability density function, the moments, skewness, and kurtosis, and limiting distributions of order statistics. Maximum likelihood estimation for the two-parameter model using complete samples is investigated. Different algorithms for generating random samples from the two new models are given. Applications to real data are discussed and compared with the fit attained by some one- and two-parameter distributions. Finally, a simulation study is carried out to investigate the mean square error of the maximum likelihood estimators, the coverage probability, and the width of the confidence intervals of the unknown parameters.http://dx.doi.org/10.1155/2014/532024 |
| spellingShingle | Ammar M. Sarhan Lotfi Tadj David C. Hamilton A New Lifetime Distribution and Its Power Transformation Journal of Probability and Statistics |
| title | A New Lifetime Distribution and Its Power Transformation |
| title_full | A New Lifetime Distribution and Its Power Transformation |
| title_fullStr | A New Lifetime Distribution and Its Power Transformation |
| title_full_unstemmed | A New Lifetime Distribution and Its Power Transformation |
| title_short | A New Lifetime Distribution and Its Power Transformation |
| title_sort | new lifetime distribution and its power transformation |
| url | http://dx.doi.org/10.1155/2014/532024 |
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