A Generalized Log-Weibull Distribution with Bio-Medical Applications
DOI:
https://doi.org/10.6000/1929-6029.2021.10.02Keywords:
Hazard rate, Maximum likelihood estimation, Model selection, Order statistics, Reliability measures, Censored dataAbstract
Here we consider a generalized log-transformed version of the Weibull distribution and investigate some of its important properties like expressions for the cumulative distribution function hazard rate function, quantile function, characteristic function, raw moments, incomplete moments, etc. The distribution and moments of order statistics are obtained along with some results on certain structural properties of the distribution. The maximum likelihood estimation of the parameters of the distribution is attempted for both complete and censored data sets and the usefulness of the distribution is illustrated with the help of real-life data sets from biomedical fields.
References
G,Elbatal I. Kumaraswamy modified inverse Weibull distribution: Theory and application. Applied Mathematics and Information Sciences 2015; 9: 651-660.
deGusmao F, Ortega E,Cordeiro G. The generalized inverse Weibull distribution. Statistical Papers 2011; 52: 591-619. https://doi.org/10.1007/s00362-009-0271-3 DOI: https://doi.org/10.1007/s00362-009-0271-3
Khan MS, King R. Modified inverse Weibull distribution. Journal of StatisticsApplications and Probability 2012; 1: 115-131. https://doi.org/10.12785/jsap/010204 DOI: https://doi.org/10.12785/jsap/010204
Kumar CS, Nair SR. On some aspects of a flexible class of additive Weibull distribution. Communications in Statistics-Theory and Methods 2018; 47: 1028-1049. https://doi.org/10.1080/03610926.2017.1316399 DOI: https://doi.org/10.1080/03610926.2017.1316399
Nassar MM,Eissa FH. On the exponentiatedWeibull distribution. Communications in Statistics-Theory and Methods 2003; 32: 1317-1336. https://doi.org/10.1081/STA-120021561 DOI: https://doi.org/10.1081/STA-120021561
Mudholkar GS,Srivastava DK. ExponentiatedWeibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 1993; 42: 299-302. https://doi.org/10.1109/24.229504 DOI: https://doi.org/10.1109/24.229504
Mudholkar GS,Srivastava DK,Freimer M. The exponentiatedWeibull family: A reanalysis of the bus-motor-failure data. Technometrics1995; 37: 436-445. https://doi.org/10.1080/00401706.1995.10484376 DOI: https://doi.org/10.1080/00401706.1995.10484376
Mudholkar GS,Hutson AD. The exponentiatedWeibull family: Some properties and a flood data application. Communications in Statistics-Theory and Methods 1996; 25: 3059-3083. https://doi.org/10.1080/03610929608831886 DOI: https://doi.org/10.1080/03610929608831886
Shittu OI,Adepoju KA. On the exponentiatedWeibull distribution for modeling wind speed in south western Nigeria. Journal of Modern Applied StatisticalMethods 2014; 13: 28-31. https://doi.org/10.22237/jmasm/1398918420 DOI: https://doi.org/10.22237/jmasm/1398918420
Kumar CS, Nair SR. On some properties of the log-Weibull distribution.Journal of Statistical and Mathematical Engineering 2018; 4: 3-10.
Gradshteyn IS,Ryzhik IM. Tables of Integrals, Series and Products. Academic Press, New York 2007.
Rinne H. The Weibull Distribution: A Handbook. CRC Press, Boca Raton 2008. https://doi.org/10.1201/9781420087444 DOI: https://doi.org/10.1201/9781420087444
Church JD, Harris B. The estimation of reliability from stress-strength relationships. Technometrics1970; 12: 49-54. https://doi.org/10.1080/00401706.1970.10488633 DOI: https://doi.org/10.1080/00401706.1970.10488633
Gupta RD,Kundu D. Exponentiated exponential family: an alternative toGamma and Weibull distributions. Biometrical Journal 2001; 43: 117-130. https://doi.org/10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R DOI: https://doi.org/10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R
Klein JP,Moeschberger ML. Survival analysis: techniques for censored and truncated data. Springer Science & Business Media, New York 2006.
Lawless JF. Statistical Models and Methods for Lifetime Data, Second Edition. John Wiley and Sons, New York 2003. https://doi.org/10.1002/9781118033005 DOI: https://doi.org/10.1002/9781118033005
Abouammoh A,Abdulghani S,Qamber I. On partial orderings and testing of new better than renewal used classes. Reliability Engineering and System Safety1994; 43: 37 - 41. https://doi.org/10.1016/0951-8320(94)90094-9 DOI: https://doi.org/10.1016/0951-8320(94)90094-9
Sickle-Santanello BJ, Farrar WB,Decenzo JF,Keyhani-Rofagha S, Klein J, Pearl D,Laufman H, O’Toole RV. Technical and statistical improvements for flow cytometric DNA analysis of paraffin-embedded tissue. Cytometry: The Journal of the International Society for Analytical Cytology1988; 9(6): 594-599. https://doi.org/10.1002/cyto.990090613 DOI: https://doi.org/10.1002/cyto.990090613
Prudnikov AP,Brychkov YA,Marichev OI. Integrals and Series(1,2 and3). Gordon and Breach Science Publishers, Amsterdam 1986.
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