The New Extended Flexible Weibull Distribution and Its Applications

Zubair Ahmad; Zawar Hussain

doi:doi:10.11648/j.ijdsa.20170303.11

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The New Extended Flexible Weibull Distribution and Its Applications

Zubair Ahmad, Zawar Hussain

Published in International Journal of Data Science and Analysis (Volume 3, Issue 3)

Received: 7 June 2017 Accepted: 11 July 2017 Published: 26 September 2017

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Abstract

The present article considers a new function to propose a new lifetime distribution. The new distribution is introduced by mixing up a linear system of the two logarithms of cumulative hazard functions. The proposed model is called new extended flexible Weibull distribution and is able to model lifetime with bathtub shaped failure rates and offers greater flexibility. Therefore, it can be quite valuable to use an alternative model to other existing lifetime distributions, where, modeling of real data sets with bathtub shaped failure rates are of interest. A brief description of the statistical properties along with estimation of the parameters through maximum likelihood procedure are discussed. The potentiality of the proposed model is showed by discussing two real data sets. For these data sets, the proposed model outclasses the Flexible Weibull Extension, Inverse Flexible Weibull Extension and Modified Weibull distributions.

Published in	International Journal of Data Science and Analysis (Volume 3, Issue 3)
DOI	10.11648/j.ijdsa.20170303.11
Page(s)	18-23
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Bathtub Shaped Failure Rates, Order Statistics, Moment Generating Function, Maximum Likelihood Estimation

References

[1]	Ahmad, Z. and Iqbal, B. (2017). Generalized Flexible Weibull Extension Distribution. Circulation in Computer Science, Volume 2(4), 68-75. https:/doi.org/10.22632/css-2017-252-11.
[2]	Ahmad, Z. and Hussain, Z. (2017). New Flexible Weibull Distribution. International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol.6, No.13.
[3]	Ahmad, Z. and Hussain, Z. (2017). Modified New Flexible Weibull Distribution. Circulation in Computer Science, Vol.2, No.6, pp: (7-13). https://doi.org/10.22632/ccs-2017-252-30.
[4]	Ahmad, Z. and Hussain, Z. (2017). New Extended Weibull Distribution. Circulation in Computer Science, Vol.2, No.6, pp: (14-19). https://doi.org/10.22632/ccs-2017-252-31.
[5]	Ahmad, Z. and Hussain, Z. (2017). Flexible Weibull Distribution. Journal of Computer and Mathematical Science, Vol.8, No.6, pp: (251-260)
[6]	Ahmad, Z. and Hussain, Z. (2017). Very Flexible Weibull Distribution. Mayfeb Journal of Mathematics. (Accepted).
[7]	Almalki, S. J. and Yuan, J. (2013). A new modified Weibull distribution. Reliability Engineering and System Safety, 111, 164–170.
[8]	Bebbington, M., Lai, C. D. and Zitikis, R. (2007). A flexible Weibull extension. Reliability Engineering and System Safety, 92, 719-726.
[9]	Carrasco M., Ortega E. M. and Cordeiro G. M. (2008). A generalized modified Weibull distribution for lifetime modeling. Computational Statistics and Data Analysis, 53(2), 450–62.
[10]	Cordeiro, G. M., Ortega, E. M. and Nadarajah, S. (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347, 1399–429.
[11]	Famoye, F., Lee, C. and Olumolade, O. (2005). The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2), 121–36.
[12]	Gurvich, M. R., Dibenedetto, A. T. and Rande, S. V. (1997). A new statistical distribution for characterizing the random length of brittle materials. J Mater Sci; 32:2559–64.
[13]	Khan, A. H. and Jan, T. R. (2016). The new modified generalized linear failure rate distribution. J. Stat. Appl. Pro.Lett. 3, No. 2, 83-95.
[14]	Murthy, D. N. P., Xie, M. and Jiang, R. (2003). Weibull Models. John Wiley and Sons, New York.
[15]	Pham, H. and Lai, C. D. (2007). On recent generalizations of the Weibull distribution. IEEE Transactions on Reliability, 56, 454–8.
[16]	Sarhan, A. M. and Apaloo, J. (2013). Exponentiated modified Weibull extension distribution. Reliability Engineering and System Safety, 112, 137–144.
[17]	Sarhan, A. M. and Zaindin, M. (2009). Modified Weibull distribution. Applied Sciences, 11, 123–136.
[18]	Tahir, M. H., Cordeiro, G. M., Mansoor, M. and Zubair, M. (2015). The Weibull-Lomax Distribution: Properties and Applications', Hacettepe Journal of Mathematics and Statistics.
[19]	Weibull, W. (1939). A statistical theory of the strength of material. Ingeniors Vetenskaps Akademiens, Stockholm 151.
[20]	Xie, M. and Lai, C. D. (1996). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering and System Safety, 52(1), 87-93.
[21]	Zwillinger, D. (2014). Table of integrals, series, and products. Elsevier.

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Zubair Ahmad, Zawar Hussain. (2017). The New Extended Flexible Weibull Distribution and Its Applications. International Journal of Data Science and Analysis, 3(3), 18-23. https://doi.org/10.11648/j.ijdsa.20170303.11

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ACS Style

Zubair Ahmad; Zawar Hussain. The New Extended Flexible Weibull Distribution and Its Applications. Int. J. Data Sci. Anal. 2017, 3(3), 18-23. doi: 10.11648/j.ijdsa.20170303.11

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AMA Style

Zubair Ahmad, Zawar Hussain. The New Extended Flexible Weibull Distribution and Its Applications. Int J Data Sci Anal. 2017;3(3):18-23. doi: 10.11648/j.ijdsa.20170303.11

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@article{10.11648/j.ijdsa.20170303.11,
  author = {Zubair Ahmad and Zawar Hussain},
  title = {The New Extended Flexible Weibull Distribution and Its Applications},
  journal = {International Journal of Data Science and Analysis},
  volume = {3},
  number = {3},
  pages = {18-23},
  doi = {10.11648/j.ijdsa.20170303.11},
  url = {https://doi.org/10.11648/j.ijdsa.20170303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20170303.11},
  abstract = {The present article considers a new function to propose a new lifetime distribution. The new distribution is introduced by mixing up a linear system of the two logarithms of cumulative hazard functions. The proposed model is called new extended flexible Weibull distribution and is able to model lifetime with bathtub shaped failure rates and offers greater flexibility. Therefore, it can be quite valuable to use an alternative model to other existing lifetime distributions, where, modeling of real data sets with bathtub shaped failure rates are of interest. A brief description of the statistical properties along with estimation of the parameters through maximum likelihood procedure are discussed. The potentiality of the proposed model is showed by discussing two real data sets. For these data sets, the proposed model outclasses the Flexible Weibull Extension, Inverse Flexible Weibull Extension and Modified Weibull distributions.},
 year = {2017}
}

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TY  - JOUR
T1  - The New Extended Flexible Weibull Distribution and Its Applications
AU  - Zubair Ahmad
AU  - Zawar Hussain
Y1  - 2017/09/26
PY  - 2017
N1  - https://doi.org/10.11648/j.ijdsa.20170303.11
DO  - 10.11648/j.ijdsa.20170303.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 18
EP  - 23
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20170303.11
AB  - The present article considers a new function to propose a new lifetime distribution. The new distribution is introduced by mixing up a linear system of the two logarithms of cumulative hazard functions. The proposed model is called new extended flexible Weibull distribution and is able to model lifetime with bathtub shaped failure rates and offers greater flexibility. Therefore, it can be quite valuable to use an alternative model to other existing lifetime distributions, where, modeling of real data sets with bathtub shaped failure rates are of interest. A brief description of the statistical properties along with estimation of the parameters through maximum likelihood procedure are discussed. The potentiality of the proposed model is showed by discussing two real data sets. For these data sets, the proposed model outclasses the Flexible Weibull Extension, Inverse Flexible Weibull Extension and Modified Weibull distributions.
VL  - 3
IS  - 3
ER  -

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Author Information

Zubair Ahmad

Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
Zawar Hussain

Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan

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APA Style

Zubair Ahmad, Zawar Hussain. (2017). The New Extended Flexible Weibull Distribution and Its Applications. International Journal of Data Science and Analysis, 3(3), 18-23. https://doi.org/10.11648/j.ijdsa.20170303.11

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ACS Style

Zubair Ahmad; Zawar Hussain. The New Extended Flexible Weibull Distribution and Its Applications. Int. J. Data Sci. Anal. 2017, 3(3), 18-23. doi: 10.11648/j.ijdsa.20170303.11

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AMA Style

Zubair Ahmad, Zawar Hussain. The New Extended Flexible Weibull Distribution and Its Applications. Int J Data Sci Anal. 2017;3(3):18-23. doi: 10.11648/j.ijdsa.20170303.11

Copy | Download

@article{10.11648/j.ijdsa.20170303.11,
  author = {Zubair Ahmad and Zawar Hussain},
  title = {The New Extended Flexible Weibull Distribution and Its Applications},
  journal = {International Journal of Data Science and Analysis},
  volume = {3},
  number = {3},
  pages = {18-23},
  doi = {10.11648/j.ijdsa.20170303.11},
  url = {https://doi.org/10.11648/j.ijdsa.20170303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20170303.11},
  abstract = {The present article considers a new function to propose a new lifetime distribution. The new distribution is introduced by mixing up a linear system of the two logarithms of cumulative hazard functions. The proposed model is called new extended flexible Weibull distribution and is able to model lifetime with bathtub shaped failure rates and offers greater flexibility. Therefore, it can be quite valuable to use an alternative model to other existing lifetime distributions, where, modeling of real data sets with bathtub shaped failure rates are of interest. A brief description of the statistical properties along with estimation of the parameters through maximum likelihood procedure are discussed. The potentiality of the proposed model is showed by discussing two real data sets. For these data sets, the proposed model outclasses the Flexible Weibull Extension, Inverse Flexible Weibull Extension and Modified Weibull distributions.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - The New Extended Flexible Weibull Distribution and Its Applications
AU  - Zubair Ahmad
AU  - Zawar Hussain
Y1  - 2017/09/26
PY  - 2017
N1  - https://doi.org/10.11648/j.ijdsa.20170303.11
DO  - 10.11648/j.ijdsa.20170303.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 18
EP  - 23
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20170303.11
AB  - The present article considers a new function to propose a new lifetime distribution. The new distribution is introduced by mixing up a linear system of the two logarithms of cumulative hazard functions. The proposed model is called new extended flexible Weibull distribution and is able to model lifetime with bathtub shaped failure rates and offers greater flexibility. Therefore, it can be quite valuable to use an alternative model to other existing lifetime distributions, where, modeling of real data sets with bathtub shaped failure rates are of interest. A brief description of the statistical properties along with estimation of the parameters through maximum likelihood procedure are discussed. The potentiality of the proposed model is showed by discussing two real data sets. For these data sets, the proposed model outclasses the Flexible Weibull Extension, Inverse Flexible Weibull Extension and Modified Weibull distributions.
VL  - 3
IS  - 3
ER  -

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