The Beta Transmuted Weibull Distribution

  • Manisha Pal University of Calcutta
  • Montip Tiensuwan Mahidol University, Bangkok

Abstract

The paper introduces a beta transmuted Weibull distribution, which contains a number of
distributions as special cases. The properties of the distribution are discussed and explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, and reliability. The distribution and moments of order statistics are also studied. Estimation of the model parameters by the method of maximum likelihood is discussed. The log beta transmuted Weibull model is introduced to analyze censored data. Finally, the usefulness of the new distribution in analyzing positive data is illustrated.

Author Biography

Manisha Pal, University of Calcutta
Professor, Department of Statistics, University of Calcutta

References

Aryall GR, Tsokos CP (2011). “Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution.” European Journal of Pure and Applied Mathematics, 4, 89–102.

Cordeira GM, Gomes AE, da-Silva CQ, Ortega EMM (2013). “The Beta Exponentiated Weibull Distribution.” Journal of Statistical Computation and Simulation, 83, 114–138.

Cordeiro GM, Nadarajah S (2011). “Closed form Expressions for Moments of a Class of Beta Generalized Distributions.” Brazilian Journal of Probability and Statistics, 25, 14–33.

Elbatal I (2011). “Exponentiated Modified Weibull Distribution.” Economic Quality Control, 26, 189–200.

Eugene N, Lee C, Famoye F (2002). “Beta-normal Distribution and its Applications.” Communications in Statistics – Theory and Methods, 31, 497–512.

Gradshteyn IS, Ryzhik IM (2000). Table of Integrals, Series, and Products. Academic Press, New York.

Hosking JRM (1990). “L-moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics.” Journal of the Royal Statistical Society (Series B), 52, 105–124.

Jones MC (2004). “Family of Distributions Arising from Distribution of Order Statistics.” Test, 13, 1–43.

Lee C, Famoye F, Olumolade O (2007). “Beta-Weibull Distribution: Some Properties and Applications to Censored Data.” Journal of Modern Applied Statistical Methods, 6, 173–186.

Mudholkar GS, Srivastava DK (1993). “Exponentiated Weibull Family for Analyzing Bathtub Failure rate Data.” IEEE Transactions on Reliability, 42, 299–302.

Nelson W (1982). Applied Life Data Analysis. John Wiley and Sons, New York.

Pal M, Masoom Ali M, Woo J (2006). “On the Exponentiated Weibull Distribution.” Statistica, 66, 139–147.

Prudnikov AP, Brychkov YA, Marichev OI (1986). Integrals and Series, volume 1. Gordon and Breach Science Publishers, Amsterdam.

Quesenberry CP, Kent J (1982). “Selecting Among Probability Distributions used in Reliability.” Technometrics, 24, 59–65.

Sarhan AM, Zaindin M (2009). “Modified Weibull Distribution.” Applied Sciences, 11, 123–136.

Silva GO, Ortega EMM, Cordeiro GM (2010). “The Beta Modified Weibull Distribution.” Lifetime Data Analysis, 16, 409–430.
Published
2014-06-13
How to Cite
Pal, M., & Tiensuwan, M. (2014). The Beta Transmuted Weibull Distribution. Austrian Journal of Statistics, 43(2), 133-149. https://doi.org/https://doi.org/10.17713/ajs.v43i2.37
Section
Articles