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Transmuted Modified Weibull Distribution: A Generalization of the Modified Weibull Probability Distribution

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2013

Key Words:

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Abstract (2. Language): 
This paper introduces a transmuted modified Weibull distribution as an important competitive model which contains eleven life time distributions as special cases. We generalized the three parameter modified Weibull distribution using the quadratic rank transmutation map studied by Shaw et al. [12] to develop a transmuted modified Weibull distribution. The properties of the transmuted modified Weibull distribution are discussed. Least square estimation is used to evaluate the parameters. Explicit expressions are derived for the quantiles. We derive the moments and examine the order statistics. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. This model is capable of modeling of various shapes of aging and failure criteria.
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  • 1
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  • English

REFERENCES

References: 

[1] G. R. Aryall and C. P. Tsokos. Transmuted Weibull distribution: A Generalization of the
Weibull Probability Distribution. European Journal of Pure and Applied Mathematics, Vol.
4, No. 2, 89-102. 2011.
[2] G. R. Aryall and C. P. Tsokos. On the transmuted extreme value distribution with applications.
Nonlinear Analysis: Theory, Methods and applications, Vol. 71, 1401-1407.
2009.
[3] R. Dumonceaux and C. Antle. Discrimination between the log-normal and the Weibull
distributions, Technometrics, 15(4), 923-926. 1973.
[4] C.-C. Liu. A Comparison between the Weibull and Lognormal Models used to Analyze
Reliability Data. PhD thesis University of Nottingham, UK. 1997.
[5] G. Mudholkar, D. Srivastava, and G. 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.
[6] M. M. Nassar and F. H. Eissa. On the Exponentiated Weibull Distribution. Communica-
tions in Statistics - Theory and Methods, 32(7):1317-1336, 2003.
[7] M. Pal, M. M. Ali, and J. Woo. On the exponentiated Weibull distribution. Statistica.
(2):139-147, 2006.
[8] H. Pham and C.-D. Lai. On Recent Generalizations of the Weibull Distribution. IEEE
Transactions on Reliability, 56(3):454-458, 2007.
[9] M. Z. Raqab. Inferences for generalized exponential distribution based on record Statistics.
Journal of Statistical Planning and Inference. Vol. 104, 2, pp. 339-350. 2002.
[10] A. M. Sarhan and M. Zaindin. Modified Weibull distribution, Applied Sciences, Vol.11,
2009, pp. 123-136. 2009.
[11] M. Shakil and M. Ahsanullah. Review on Order Statistics and Record Values from F
Distributions. Pakistan Journal of Statistics and Operation Research. Vol. VIII No.1, pp.
101-120. 2012.
REFERENCES 87
[12] 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.
[13] M. Zaindin and A. M. Sarhan. Parameters Estimation of the Modified Weibull Distribution,
Applied Mathematical Sciences, Vol. 3, no. 11, 541-550. 2009.

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