Transmuted Weibull distribution: a generalization of the Weibull probability distribution
In this article, the two parameter Weibull probability distribution is embedded in a larger family obtained by introducing an additional parameter. We generalize the two parameter Weibull distribution using the quadratic rank transmutation map studied by Shaw et al. [9] to develop a transmuted Weibu...
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| Published in | European journal of pure and applied mathematics Vol. 4; no. 2; pp. 89 - 102 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
xxx
2011
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| Online Access | Get full text |
| ISSN | 1307-5543 1307-5543 |
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| Abstract | In this article, the two parameter Weibull probability distribution is embedded in a larger
family obtained by introducing an additional parameter. We generalize the two parameter Weibull
distribution using the quadratic rank transmutation map studied by Shaw et al. [9] to develop a transmuted
Weibull distribution. We provide a comprehensive description of the mathematical properties
of the subject distribution along with its reliability behavior. The usefulness of the transmuted Weibull
distribution for modeling reliability data is illustrated using real data.
2000 Mathematics Subject Classifications: 62N05; 90B25 |
|---|---|
| AbstractList | In this article, the two parameter Weibull probability distribution is embedded in a larger
family obtained by introducing an additional parameter. We generalize the two parameter Weibull
distribution using the quadratic rank transmutation map studied by Shaw et al. [9] to develop a transmuted
Weibull distribution. We provide a comprehensive description of the mathematical properties
of the subject distribution along with its reliability behavior. The usefulness of the transmuted Weibull
distribution for modeling reliability data is illustrated using real data.
2000 Mathematics Subject Classifications: 62N05; 90B25 |
| Author | ARYAL, Gokarna R TSOKOS, Chris P |
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| References | M. D. Nichols andW.J. Padgett. A bootstrap control chart forWeibull percentiles. Quality and Reliability Engineering International, 22:141-151, 2006. Gokarna R. Aryal and Chris P. Tsokos. On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods and Applications, 71:1401-1407, 2009. Hoang Pham and Chin-Diew Lai. On Recent Generalizations of the Weibull Distribution. IEEE Transactions on RELIABILITY, 56(3):454-458, 2007. M. Pal, M. M. Ali, and J. Woo. On the exponentiated weibull distribution. Statistica., (2):139-147, 2006. C. P. Quesenberry and Jacqueline Kent. Selecting Among Probability Distributions Used in Reliability. Technometrics, 24(1):59-65, 1982. Manal M. Nassar and Fathy H. Eissa. On the Exponentiated Weibull Distribution. Communications in Statistics - Theory and Methods, 32(7):1317-1336, 2003. R. Ihaka and R. Gentleman. R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5:299-314, 1996. M. Zaindin and Ammar M. Sarhan. Parameters Estimation of the Modified Weibull Distribution. Applied Mathematical Sciences, 3(11):541-550, 2009. Govinda Mudholkar, Deo Srivastava, and George Kollia. A generalization of the weibull distribution with application to the analysis of survival data. Journal of the American Statistical Association, 91(436):1575-1583, 1996. W. Shaw and I. Buckley. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map.. Research report, 2007. |
| References_xml | – reference: M. Pal, M. M. Ali, and J. Woo. On the exponentiated weibull distribution. Statistica., (2):139-147, 2006. – reference: C. P. Quesenberry and Jacqueline Kent. Selecting Among Probability Distributions Used in Reliability. Technometrics, 24(1):59-65, 1982. – reference: M. Zaindin and Ammar M. Sarhan. Parameters Estimation of the Modified Weibull Distribution. Applied Mathematical Sciences, 3(11):541-550, 2009. – reference: Manal M. Nassar and Fathy H. Eissa. On the Exponentiated Weibull Distribution. Communications in Statistics - Theory and Methods, 32(7):1317-1336, 2003. – reference: R. Ihaka and R. Gentleman. R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5:299-314, 1996. – reference: Gokarna R. Aryal and Chris P. Tsokos. On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods and Applications, 71:1401-1407, 2009. – reference: Govinda Mudholkar, Deo Srivastava, and George Kollia. A generalization of the weibull distribution with application to the analysis of survival data. Journal of the American Statistical Association, 91(436):1575-1583, 1996. – reference: W. Shaw and I. Buckley. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map.. Research report, 2007. – reference: M. D. Nichols andW.J. Padgett. A bootstrap control chart forWeibull percentiles. Quality and Reliability Engineering International, 22:141-151, 2006. – reference: Hoang Pham and Chin-Diew Lai. On Recent Generalizations of the Weibull Distribution. IEEE Transactions on RELIABILITY, 56(3):454-458, 2007. |
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