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A New Discrete Family of Reduced Modified Weibull Distribution

Received: 16 August 2017     Accepted: 31 August 2017     Published: 26 October 2017
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Abstract

Discretization of continuous lifetime distribution is an interesting and intuitively appealing approach to derive a discrete lifetime model. This study derived a discretized form of Reduced Modified Weibull distribution known as the Marshall-Olkin Discrete Reduced Modified Weibull (MDRMW) distribution. The mathematical and statistical properties of MDRMW distribution were derived and compared with existing distributions of Discrete Reduced Modified Weibull distribution (DRMW), Exponentiated Discrete Weibull distribution (EDW) and Two Parameters Discrete Lindley distribution (TDL). Maximum likelihood method was used to derive the statistics of MDRMW parameters. The Aarset Reliability dataset was fitted for the existing and derived distribution and AIC and Kolmogorov Smirrnoff (KS) were compared. The shape of MDRMW distribution was unimodal and monotonic decreasing. The plot of hazard rate function could be decreasing or bath-tub. The AIC and KS values of Aarset reliability data analysis were 483.9 and 0.17579; 507.8 and 0.24435; 485.2 and 0.17897 for MDRMW, DRMW and TDL respectively. The AIC and KS values of Leukemia survival data analysis were 668.2 and 0.11053; 751.9 and 0.39285 respectively. The Aarset reliability data analysis showed that MDRMW compared favorably with existing distributions. The MDRMW and DRMW handled Leukemia survival data set as against EDW and TDL. The values of AIC and KS for MDRMW were lower than DRMW, EDW and TDL. This showed that MDRMW was better than the existing distributions.

Published in International Journal of Statistical Distributions and Applications (Volume 3, Issue 3)
DOI 10.11648/j.ijsd.20170303.11
Page(s) 25-31
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), 2017. Published by Science Publishing Group

Keywords

Weibull, TDL, DRMW, EDW, MDRMW

References
[1] Almalki, S. J. (2014). Statistical analysis of lifetime data using new modified Weibull distributions, a thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences.
[2] Bebbington, M., Lai, C. D. and Zitikis, R. (2007). A flexible Weibull extension. Reliability Engineering and System Safety, 92, 719-726.
[3] Comtet, L. (1974). Advanced Combinatorics: The art of finite and infinite expansions. Springer.
[4] Marshall, A. W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84(3), 641-652.
[5] Mudholkar, G. S. and Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. Reliability, IEEE Transactions on, 42(2), 299-302.
[6] Nooghabi, M. S., Roknabadi, A. H. R. and Borzadaran, G. M. (2011). Discrete modified Weibull distribution. Metron, LXIX, 207–222.
[7] p-value calculator online: https://graphpad.com/quickcalcs/PValue1.cfm (2017)
[8] Stein, W. E. and Dattero, R. (1984). A new discrete Weibull distribution. Reliability, IEEE Transactions on, 33(2), 196-197.
[9] Tassaddaq, H., Muhammad, A and Munir A. (2016). A Two Parameter Discrete Lindley Distribution January 2016, Volume 39, Issue 1, pp. 45 to 61 DOI.
[10] Zhang, T. and Xie, M. (2011). On the upper truncated Weibull distribution and its reliability implications. Reliability Engineering and System Safety, 96(1), 194-200.
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  • APA Style

    Ademola Lateef Oloko, Osebekwin Ebenezer Asiribo, Ganiyu Abayomi Dawodu, Mathew Omonigho Omeike, Nurudeen Ayobami Ajadi, et al. (2017). A New Discrete Family of Reduced Modified Weibull Distribution. International Journal of Statistical Distributions and Applications, 3(3), 25-31. https://doi.org/10.11648/j.ijsd.20170303.11

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    ACS Style

    Ademola Lateef Oloko; Osebekwin Ebenezer Asiribo; Ganiyu Abayomi Dawodu; Mathew Omonigho Omeike; Nurudeen Ayobami Ajadi, et al. A New Discrete Family of Reduced Modified Weibull Distribution. Int. J. Stat. Distrib. Appl. 2017, 3(3), 25-31. doi: 10.11648/j.ijsd.20170303.11

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    AMA Style

    Ademola Lateef Oloko, Osebekwin Ebenezer Asiribo, Ganiyu Abayomi Dawodu, Mathew Omonigho Omeike, Nurudeen Ayobami Ajadi, et al. A New Discrete Family of Reduced Modified Weibull Distribution. Int J Stat Distrib Appl. 2017;3(3):25-31. doi: 10.11648/j.ijsd.20170303.11

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  • @article{10.11648/j.ijsd.20170303.11,
      author = {Ademola Lateef Oloko and Osebekwin Ebenezer Asiribo and Ganiyu Abayomi Dawodu and Mathew Omonigho Omeike and Nurudeen Ayobami Ajadi and Abayomi Olumuyiwa Ajayi},
      title = {A New Discrete Family of Reduced Modified Weibull Distribution},
      journal = {International Journal of Statistical Distributions and Applications},
      volume = {3},
      number = {3},
      pages = {25-31},
      doi = {10.11648/j.ijsd.20170303.11},
      url = {https://doi.org/10.11648/j.ijsd.20170303.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20170303.11},
      abstract = {Discretization of continuous lifetime distribution is an interesting and intuitively appealing approach to derive a discrete lifetime model. This study derived a discretized form of Reduced Modified Weibull distribution known as the Marshall-Olkin Discrete Reduced Modified Weibull (MDRMW) distribution. The mathematical and statistical properties of MDRMW distribution were derived and compared with existing distributions of Discrete Reduced Modified Weibull distribution (DRMW), Exponentiated Discrete Weibull distribution (EDW) and Two Parameters Discrete Lindley distribution (TDL). Maximum likelihood method was used to derive the statistics of MDRMW parameters. The Aarset Reliability dataset was fitted for the existing and derived distribution and AIC and Kolmogorov Smirrnoff (KS) were compared. The shape of MDRMW distribution was unimodal and monotonic decreasing. The plot of hazard rate function could be decreasing or bath-tub. The AIC and KS values of Aarset reliability data analysis were 483.9 and 0.17579; 507.8 and 0.24435; 485.2 and 0.17897 for MDRMW, DRMW and TDL respectively. The AIC and KS values of Leukemia survival data analysis were 668.2 and 0.11053; 751.9 and 0.39285 respectively. The Aarset reliability data analysis showed that MDRMW compared favorably with existing distributions. The MDRMW and DRMW handled Leukemia survival data set as against EDW and TDL. The values of AIC and KS for MDRMW were lower than DRMW, EDW and TDL. This showed that MDRMW was better than the existing distributions.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - A New Discrete Family of Reduced Modified Weibull Distribution
    AU  - Ademola Lateef Oloko
    AU  - Osebekwin Ebenezer Asiribo
    AU  - Ganiyu Abayomi Dawodu
    AU  - Mathew Omonigho Omeike
    AU  - Nurudeen Ayobami Ajadi
    AU  - Abayomi Olumuyiwa Ajayi
    Y1  - 2017/10/26
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ijsd.20170303.11
    DO  - 10.11648/j.ijsd.20170303.11
    T2  - International Journal of Statistical Distributions and Applications
    JF  - International Journal of Statistical Distributions and Applications
    JO  - International Journal of Statistical Distributions and Applications
    SP  - 25
    EP  - 31
    PB  - Science Publishing Group
    SN  - 2472-3509
    UR  - https://doi.org/10.11648/j.ijsd.20170303.11
    AB  - Discretization of continuous lifetime distribution is an interesting and intuitively appealing approach to derive a discrete lifetime model. This study derived a discretized form of Reduced Modified Weibull distribution known as the Marshall-Olkin Discrete Reduced Modified Weibull (MDRMW) distribution. The mathematical and statistical properties of MDRMW distribution were derived and compared with existing distributions of Discrete Reduced Modified Weibull distribution (DRMW), Exponentiated Discrete Weibull distribution (EDW) and Two Parameters Discrete Lindley distribution (TDL). Maximum likelihood method was used to derive the statistics of MDRMW parameters. The Aarset Reliability dataset was fitted for the existing and derived distribution and AIC and Kolmogorov Smirrnoff (KS) were compared. The shape of MDRMW distribution was unimodal and monotonic decreasing. The plot of hazard rate function could be decreasing or bath-tub. The AIC and KS values of Aarset reliability data analysis were 483.9 and 0.17579; 507.8 and 0.24435; 485.2 and 0.17897 for MDRMW, DRMW and TDL respectively. The AIC and KS values of Leukemia survival data analysis were 668.2 and 0.11053; 751.9 and 0.39285 respectively. The Aarset reliability data analysis showed that MDRMW compared favorably with existing distributions. The MDRMW and DRMW handled Leukemia survival data set as against EDW and TDL. The values of AIC and KS for MDRMW were lower than DRMW, EDW and TDL. This showed that MDRMW was better than the existing distributions.
    VL  - 3
    IS  - 3
    ER  - 

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Author Information
  • Department of Statistics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Ogun, Nigeria

  • Department of Statistics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Ogun, Nigeria

  • Department of Statistics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Ogun, Nigeria

  • Department of Statistics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Ogun, Nigeria

  • Department of Statistics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Ogun, Nigeria

  • Department of Statistics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Ogun, Nigeria

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