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Year 2018, Volume: 47 Issue: 6, 1671 - 1689, 12.12.2018

Abstract

References

  • Aarset, A.S. How to identify a bathtub hazard rate, IEEE Transactions on Reliability 36, 106-108, 1987.
  • Afify A.Z., Alizadeh, M., Yousof, H.M., Aryal, G. and Ahmad, M. The transmuted geometric-G family of distributions: theory and applications, Pak. J. Statist. 32 (2), 139-160, 2016a.
  • Afify A.Z., Cordeiro, G.M., Yousof, H.M., Alzaatreh, A. and Nofal, Z.M. The Kumaraswamy transmuted-G family of distributions: properties and applications, J. Data Sci. 14 , 245-270, 2016b.
  • Afify, A.Z., Yousof, H.M. and Nadarajah, S. The beta transmuted-H family of distributions: properties and applications, Stasistics and its Inference 10 (3), 505-520, 2017.
  • Alizadeh, M., Cordeiro, G.M., de Brito, E. and Dem\'{e}trio C.G.B. The beta Marshall-Olkin family of distributions, Journal of Statistical Distributions and Applications 2 (4) , 18-page, 2015a.
  • Alizadeh, M., Cordeiro, G.M., Mansoor, M., Zubair, M. and Hamedani, G.G. The Kumaraswamy Marshal-Olkin family of distributions, Journal of the Egyptian Mathematical Society 23 , 546-557, 2015c.
  • Alizadeh, M., Cordeiro, G.M., Nascimento, A.D.C. Lima M.D.S. and Ortega, E.M.M. Odd-Burr generalized family of distributions with some applications, Journal of Statistical Computation and Simulation 83 , 326-339, 2016a.
  • Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G.M., Ortega, E.M.M. and Pescim, R.R. Kumaraswamy odd log-logistic family of distributions: Properties and applications, Hacettepe Journal of Mathematics and Statistics 44 (6) , 1491-1512, 2015a.
  • Alizadeh, M., Merovci, F. and Hamedani, G.G. Generalized transmuted family of distributions: properties and applications, Hacettepe Journal of Mathematics and Statistics forthcomig., 2015d.
  • Alizadeh, M., Yousof, H.M., Afify A.Z., Cordeiro, G.M., and Mansoor, M. The complementary generalized transmuted poisson-G family, Austrian Journal of Statistics 47 , 51-71, 2018.
  • Alkarni, S.H. Extended power Lindley distribution: A new statistical model for nonmonotone survival data, European Journal of Statistics and Probability 3 , 19-34, 2015.
  • Alzaghal, A., Famoye, F. and Lee, C. Exponentiated T-X family of distributions with some applications, International Journal of Probability and Statistics 2 , 31-49, 2013.
  • Alzaatreh, A., Lee, C. and Famoye, F. A new method for generating families of continuous distributions, Metron 71, 63-79, 2013.
  • Bakouch, H.S., Al-Zahrani, B.M., Al-Shomrani, A.A., Marchi, V.A.A. and Louzada, F. An extended Lindley distribution, Journal of the Korean Statistical Society 41, 75-85, 2012.
  • Bourguignon, M., Silva, R.B. and Cordeiro, G.M. The Weibull-G family of probability distributions, Journal of Data Science 12 (1), 53-68, 2014.
  • Cordeiro, G.M., Alizadeh, M. and Diniz Marinho, P.R. The type I half-logistic family of distributions, Journal of Statistical Computation and Simulation 86, 707-728, 2016b.
  • Cordeiro, G.M., Alizadeh, M., Ortega, E.M.M. and Serrano, L.H.V. The Zografos-Balakrishnan odd log-logistic family of distributions: Properties and Applications, Hacettepe Journal of Mathematics and Statistics, 45, 2015c.
  • Cordeiro, G.M., Alizadeh, M., Tahir, M.H., Mansoor, M., Bourguignon, M. and Hamedani, G.G. The beta odd log-logistic family of distributions, Hacettepe Journal of Mathematics and Statistics, 45, 1175-1202, 2016.
  • Cordeiro, G.M. and de Castro, M. A new family of generalized distributions, Journal of Statistical Computation and Simulation 81, 883-898, 2011.
  • Cordeiro, G.M., Gomes, A.E., da-Silva, C.Q. and Ortega, E.M.M. The beta exponentiated Weibull distribution, Journal of Statistical Computation and Simulation 83, 114-138, 2013a.
  • Cordeiro, G.M., Ortega, E.M.M. and Nadarajah, S. The Kumaraswamy Weibull distribution with application to failure data, Journal of the Franklin Institute 347, 1317-1336, 2010.
  • Cordeiro, G.M., Ortega, E.M. and da Cunha, D.C.C. The exponentiated generalized class of distributions, J. Data Sci. 11, 1-27, 2013b.
  • Cordeiro, G.M., Ortega, E.M., Popovi\'{c} B.V. and Pescim, R.R. The Lomax generator of distributions: Properties, minification process and regression model, Applied Mathematics and Computation 247, 465-486, 2014.
  • Cordeiro, G.M., Saboor, A., Nauman Khan, M. and Pascoa, M.A.R. The Kumaraswamy Exponential-Weibull Distribution: Theory and Applications, Hacettepe Journal of Mathematics and Statistics 45, 1-27, 2016a.
  • Eugene, N., Lee, C. and Famoye, F. Beta-normal distribution and its applications, Commun. Stat. Theory Methods 31, 497-512, 2002.
  • Famoye, F., Lee, C. and Olumolade, O. The Beta-Weibull Distribution, Journal of Statistical Theory and Applications 4, 121-136, 2005.
  • Gl\"{a}nzel, W. A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 75-84, 1987.
  • Gl\"{a}nzel, W. Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics 21, 613-618, 1990.
  • Gupta, R.C., Gupta, P.L. and Gupta, R.D. Modeling failure time data by Lehmann alternatives, Commun. Stat. Theory Methods 27, 887-904, 1998.
  • Lee, C., Famoye, F. and Olumolade, O. Beta-Weibull Distribution: Some Properties and Applications to Censored Data, Journal of Modern Applied Statistical Methods 6, 173-186, 2007.
  • Marshall, A. W. and Olkin, I. A new methods for adding a parameter to a family of distributions with application to the Exponential and Weibull families. Biometrika, 84, 641-652, 1997.
  • Merovci, F., Alizadeh, M. and Hamedani, G. G. Another generalized transmuted family of distributions: properties and applications, Austrian Journal of Statistics, 45, 71-93, 2015.
  • Merovci, F., Alizadeh, M., Yousof, H. M. and Hamedani, G. G. The exponentiated transmuted-G family of distributions: Theory and applications, Communications in Statistics-Theory and Methods, 46 (21), 10800-10822, 2017.
  • Murthy, D. P., Xie, M. and Jiang, R. Weibull models (Vol. 505). John Wiley and Sons, 2004.
  • Nadarajah, S. and Kotz, S. Strength modeling using Weibull distributions. Journal of Mechanical Science and Technology, 22, 1247-1254, 2008.
  • Nofal, Z. M., Afify, A. Z., Yousof, H. M. and Cordeiro, G. M. The generalized transmuted-G family of distributions. Communications in Statistics-Theory and Methods, 46 (8), 4119-4136, 2017.
  • Ramos, M.W.A., Marinho, P.R.D., da Silva R.V. and Cordeiro, G.M. The exponentiated Lomax Poisson distribution with an application to lifetime data. Advances and Applications in Statistics, 34, 107-135, 2013.
  • Rezaei, S., Sadr, B.B., Alizadeh, M. and Nadarajah, S. Topp-Leone generated family of distributions: Properties and applications, Communications in Statistics-Theory and Methods, 46 (7), 2893-2909, 2016.
  • Shaw, W. T. and Buckley, I. R. C. The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research report, 2007.
  • Silva, G.O., Ortega, E.M.M. and Cordeiro, G.M. The beta modified Weibull distribution. Lifetime Data Analysis, 16, 409-430, 2010.
  • Warahena-Liyanage, G. and Pararai, M. A generalized power Lindley distribution with applications. Asian Journal of Mathematics and Applications, 2014, 1-23, 2014.
  • Yousof, Haitham M., Ahmed Z. Afify, Morad Alizadeh, Nadeem Shafique Butt, and Gholamhossein Hamedani. The transmuted exponentiated generalized-G family of distributions. Pakistan Journal of Statistics and Operation Research, 2015.
  • Yousof, H. M., Afify, A. Z., Hamedani, G. G. and Aryal, G. The Burr X generator of distributions for lifetime data. Journal of Statistical Theory and Applications, 16, 1-19, 2016.
  • Zakerzadeh and H., Dolati, A. Generalized Lindley distribution. Journal of Mathematical Extension, 3, 13-25, 2009.
  • Zografos, K. and Balakrishnan, N. On families of beta and generalized gamma-generated distributions and associated inference. Statistical Methodology, 6, 344-362, 2009.

The transmuted Weibull-G family of distributions

Year 2018, Volume: 47 Issue: 6, 1671 - 1689, 12.12.2018

Abstract

We introduce a new family of continuous distributions called the transmuted Weibull-G family of distributions which extends the transmuted class pioneered by Shaw and Buckley (2007). We study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments as well as based on hazard function are presented. We estimate the model parameters by the maximum likelihood method. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study.

References

  • Aarset, A.S. How to identify a bathtub hazard rate, IEEE Transactions on Reliability 36, 106-108, 1987.
  • Afify A.Z., Alizadeh, M., Yousof, H.M., Aryal, G. and Ahmad, M. The transmuted geometric-G family of distributions: theory and applications, Pak. J. Statist. 32 (2), 139-160, 2016a.
  • Afify A.Z., Cordeiro, G.M., Yousof, H.M., Alzaatreh, A. and Nofal, Z.M. The Kumaraswamy transmuted-G family of distributions: properties and applications, J. Data Sci. 14 , 245-270, 2016b.
  • Afify, A.Z., Yousof, H.M. and Nadarajah, S. The beta transmuted-H family of distributions: properties and applications, Stasistics and its Inference 10 (3), 505-520, 2017.
  • Alizadeh, M., Cordeiro, G.M., de Brito, E. and Dem\'{e}trio C.G.B. The beta Marshall-Olkin family of distributions, Journal of Statistical Distributions and Applications 2 (4) , 18-page, 2015a.
  • Alizadeh, M., Cordeiro, G.M., Mansoor, M., Zubair, M. and Hamedani, G.G. The Kumaraswamy Marshal-Olkin family of distributions, Journal of the Egyptian Mathematical Society 23 , 546-557, 2015c.
  • Alizadeh, M., Cordeiro, G.M., Nascimento, A.D.C. Lima M.D.S. and Ortega, E.M.M. Odd-Burr generalized family of distributions with some applications, Journal of Statistical Computation and Simulation 83 , 326-339, 2016a.
  • Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G.M., Ortega, E.M.M. and Pescim, R.R. Kumaraswamy odd log-logistic family of distributions: Properties and applications, Hacettepe Journal of Mathematics and Statistics 44 (6) , 1491-1512, 2015a.
  • Alizadeh, M., Merovci, F. and Hamedani, G.G. Generalized transmuted family of distributions: properties and applications, Hacettepe Journal of Mathematics and Statistics forthcomig., 2015d.
  • Alizadeh, M., Yousof, H.M., Afify A.Z., Cordeiro, G.M., and Mansoor, M. The complementary generalized transmuted poisson-G family, Austrian Journal of Statistics 47 , 51-71, 2018.
  • Alkarni, S.H. Extended power Lindley distribution: A new statistical model for nonmonotone survival data, European Journal of Statistics and Probability 3 , 19-34, 2015.
  • Alzaghal, A., Famoye, F. and Lee, C. Exponentiated T-X family of distributions with some applications, International Journal of Probability and Statistics 2 , 31-49, 2013.
  • Alzaatreh, A., Lee, C. and Famoye, F. A new method for generating families of continuous distributions, Metron 71, 63-79, 2013.
  • Bakouch, H.S., Al-Zahrani, B.M., Al-Shomrani, A.A., Marchi, V.A.A. and Louzada, F. An extended Lindley distribution, Journal of the Korean Statistical Society 41, 75-85, 2012.
  • Bourguignon, M., Silva, R.B. and Cordeiro, G.M. The Weibull-G family of probability distributions, Journal of Data Science 12 (1), 53-68, 2014.
  • Cordeiro, G.M., Alizadeh, M. and Diniz Marinho, P.R. The type I half-logistic family of distributions, Journal of Statistical Computation and Simulation 86, 707-728, 2016b.
  • Cordeiro, G.M., Alizadeh, M., Ortega, E.M.M. and Serrano, L.H.V. The Zografos-Balakrishnan odd log-logistic family of distributions: Properties and Applications, Hacettepe Journal of Mathematics and Statistics, 45, 2015c.
  • Cordeiro, G.M., Alizadeh, M., Tahir, M.H., Mansoor, M., Bourguignon, M. and Hamedani, G.G. The beta odd log-logistic family of distributions, Hacettepe Journal of Mathematics and Statistics, 45, 1175-1202, 2016.
  • Cordeiro, G.M. and de Castro, M. A new family of generalized distributions, Journal of Statistical Computation and Simulation 81, 883-898, 2011.
  • Cordeiro, G.M., Gomes, A.E., da-Silva, C.Q. and Ortega, E.M.M. The beta exponentiated Weibull distribution, Journal of Statistical Computation and Simulation 83, 114-138, 2013a.
  • Cordeiro, G.M., Ortega, E.M.M. and Nadarajah, S. The Kumaraswamy Weibull distribution with application to failure data, Journal of the Franklin Institute 347, 1317-1336, 2010.
  • Cordeiro, G.M., Ortega, E.M. and da Cunha, D.C.C. The exponentiated generalized class of distributions, J. Data Sci. 11, 1-27, 2013b.
  • Cordeiro, G.M., Ortega, E.M., Popovi\'{c} B.V. and Pescim, R.R. The Lomax generator of distributions: Properties, minification process and regression model, Applied Mathematics and Computation 247, 465-486, 2014.
  • Cordeiro, G.M., Saboor, A., Nauman Khan, M. and Pascoa, M.A.R. The Kumaraswamy Exponential-Weibull Distribution: Theory and Applications, Hacettepe Journal of Mathematics and Statistics 45, 1-27, 2016a.
  • Eugene, N., Lee, C. and Famoye, F. Beta-normal distribution and its applications, Commun. Stat. Theory Methods 31, 497-512, 2002.
  • Famoye, F., Lee, C. and Olumolade, O. The Beta-Weibull Distribution, Journal of Statistical Theory and Applications 4, 121-136, 2005.
  • Gl\"{a}nzel, W. A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 75-84, 1987.
  • Gl\"{a}nzel, W. Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics 21, 613-618, 1990.
  • Gupta, R.C., Gupta, P.L. and Gupta, R.D. Modeling failure time data by Lehmann alternatives, Commun. Stat. Theory Methods 27, 887-904, 1998.
  • Lee, C., Famoye, F. and Olumolade, O. Beta-Weibull Distribution: Some Properties and Applications to Censored Data, Journal of Modern Applied Statistical Methods 6, 173-186, 2007.
  • Marshall, A. W. and Olkin, I. A new methods for adding a parameter to a family of distributions with application to the Exponential and Weibull families. Biometrika, 84, 641-652, 1997.
  • Merovci, F., Alizadeh, M. and Hamedani, G. G. Another generalized transmuted family of distributions: properties and applications, Austrian Journal of Statistics, 45, 71-93, 2015.
  • Merovci, F., Alizadeh, M., Yousof, H. M. and Hamedani, G. G. The exponentiated transmuted-G family of distributions: Theory and applications, Communications in Statistics-Theory and Methods, 46 (21), 10800-10822, 2017.
  • Murthy, D. P., Xie, M. and Jiang, R. Weibull models (Vol. 505). John Wiley and Sons, 2004.
  • Nadarajah, S. and Kotz, S. Strength modeling using Weibull distributions. Journal of Mechanical Science and Technology, 22, 1247-1254, 2008.
  • Nofal, Z. M., Afify, A. Z., Yousof, H. M. and Cordeiro, G. M. The generalized transmuted-G family of distributions. Communications in Statistics-Theory and Methods, 46 (8), 4119-4136, 2017.
  • Ramos, M.W.A., Marinho, P.R.D., da Silva R.V. and Cordeiro, G.M. The exponentiated Lomax Poisson distribution with an application to lifetime data. Advances and Applications in Statistics, 34, 107-135, 2013.
  • Rezaei, S., Sadr, B.B., Alizadeh, M. and Nadarajah, S. Topp-Leone generated family of distributions: Properties and applications, Communications in Statistics-Theory and Methods, 46 (7), 2893-2909, 2016.
  • Shaw, W. T. and Buckley, I. R. C. The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research report, 2007.
  • Silva, G.O., Ortega, E.M.M. and Cordeiro, G.M. The beta modified Weibull distribution. Lifetime Data Analysis, 16, 409-430, 2010.
  • Warahena-Liyanage, G. and Pararai, M. A generalized power Lindley distribution with applications. Asian Journal of Mathematics and Applications, 2014, 1-23, 2014.
  • Yousof, Haitham M., Ahmed Z. Afify, Morad Alizadeh, Nadeem Shafique Butt, and Gholamhossein Hamedani. The transmuted exponentiated generalized-G family of distributions. Pakistan Journal of Statistics and Operation Research, 2015.
  • Yousof, H. M., Afify, A. Z., Hamedani, G. G. and Aryal, G. The Burr X generator of distributions for lifetime data. Journal of Statistical Theory and Applications, 16, 1-19, 2016.
  • Zakerzadeh and H., Dolati, A. Generalized Lindley distribution. Journal of Mathematical Extension, 3, 13-25, 2009.
  • Zografos, K. and Balakrishnan, N. On families of beta and generalized gamma-generated distributions and associated inference. Statistical Methodology, 6, 344-362, 2009.
There are 45 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Morad Alizadeh This is me

Mahdi Rasekhi

Haitham M. Yousof

G.g. Hamedani

Publication Date December 12, 2018
Published in Issue Year 2018 Volume: 47 Issue: 6

Cite

APA Alizadeh, M., Rasekhi, M., Yousof, H. M., Hamedani, G. (2018). The transmuted Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics, 47(6), 1671-1689.
AMA Alizadeh M, Rasekhi M, Yousof HM, Hamedani G. The transmuted Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics. December 2018;47(6):1671-1689.
Chicago Alizadeh, Morad, Mahdi Rasekhi, Haitham M. Yousof, and G.g. Hamedani. “The Transmuted Weibull-G Family of Distributions”. Hacettepe Journal of Mathematics and Statistics 47, no. 6 (December 2018): 1671-89.
EndNote Alizadeh M, Rasekhi M, Yousof HM, Hamedani G (December 1, 2018) The transmuted Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics 47 6 1671–1689.
IEEE M. Alizadeh, M. Rasekhi, H. M. Yousof, and G. Hamedani, “The transmuted Weibull-G family of distributions”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1671–1689, 2018.
ISNAD Alizadeh, Morad et al. “The Transmuted Weibull-G Family of Distributions”. Hacettepe Journal of Mathematics and Statistics 47/6 (December 2018), 1671-1689.
JAMA Alizadeh M, Rasekhi M, Yousof HM, Hamedani G. The transmuted Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics. 2018;47:1671–1689.
MLA Alizadeh, Morad et al. “The Transmuted Weibull-G Family of Distributions”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, 2018, pp. 1671-89.
Vancouver Alizadeh M, Rasekhi M, Yousof HM, Hamedani G. The transmuted Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics. 2018;47(6):1671-89.