Research Article
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Year 2019, Volume: 68 Issue: 2, 1506 - 1527, 01.08.2019
https://doi.org/10.31801/cfsuasmas.542988

Abstract

References

  • Aarset, M. V., How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36, (1987), 106-108.
  • Alexander, C., Cordeiro, G. M., Ortega, E. M. and Sarabia, J. M., Generalized beta-generated distributions. Computational Statistics and Data Analysis, 56(6), (2012), 1880-1897.
  • Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G.M., Ortega, E.M.M. and Pescim, R.R., The Kumaraswamy odd log-logistic family of distributions, Hacettepe Journal of Mathematics and Statistics, 44, (2015), 1491-1512.
  • 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, (2016a), 1781-1803.
  • Cordeiro, G.M., Alizadeh, M., Tahir, M. H., Mansoor, M., Bourguignon, M. and Hamedani G.G., The beta dd log-logistic generalized family of distributions, Hacettepe Journal of Mathematics and Statistics, 45, (2016b), 1175-1202.
  • Cordeiro, G.M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E.M.M. and Altun, E., The generalized odd log-logistic family of distributions: properties, regression models and applications, Journal of Statistical Computation and Simulation, 87, (2017), 908-932.
  • Braga, A.S., Cordeiro, G. M., Ortega, E. M. and Nilton da Cruz, J., The odd log-logistic normal distribution: Theory and applications in analysis of experiments. Journal of Statistical Theory and Practice, 10(2), (2016), 311-335.
  • Brito, E., Cordeiro, G. M., Yousof, H. M., Alizadeh, M.and Silva, G. O., The Topp-Leone odd log-logistic family of distributions. Journal of Statistical Computation and Simulation, 87, (2017), 3040-3058.
  • Chen, G. and Balakrishnan, N., A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27, (1995) 154-161.
  • Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E. M. M. and Altun, E., The generalized odd log-logistic family of distributions: properties, regression models and applications. Journal of Statistical Computation and Simulation, 87, (2017), 908-932.
  • Cordeiro, G. M. and de Castro, M., A new family of generalized distributions. Journal of statistical computation and simulation, 81, (2011), 883-898.
  • Cordeiro, G. M., Ortega, E. M. and Nadarajah, S., The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347, (2010), 1399-1429.
  • Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31, (2002), 497-512.
  • Evans, D. L., Drew, J. H. and Leemis, L. M., The distribution of the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling test statistics for exponential populations with estimated parameters. Communications in Statistics-Simulation and Computation, 37, (2008) 1396-1421.
  • Famoye, F., Lee, C. and Olumolade, O., The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4, (2005), 121-136.
  • Garcia, V. J., Gomez-Deniz, E. and Vazquez-Polo, F. J., A new skew generalization of the normal distribution: Properties and applications. Computational Statistics & Data Analysis, 54(8), (2010), 2021-2034.
  • Genç, A., Moments of order statistics of Topp Leone distribution. Statistical Papers, 51, (2012) , 1-15.
  • Genç, A., Estimation of the Prob(X > Y) with Topp Leone distribution. Journal of Statistical Computation and Simulation, 83, (2013), 326-339.
  • Ghitany, M. E., Kotz, S., Xie, M., On some reliability measures and their stochastic orderings for the Topp Leone distribution. Journal of Applied Statistics, 32, (2005), 715-722.
  • Glänzel, 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, (1987), 75--84.
  • Glänzel, W., Some consequences of a characterization theorem based on truncated moments. Statistics: A Journal of Theoretical and Applied Statistics, 21, (1990), 613-618.
  • Gleaton, J. U. and Lynch, J. D., Properties of generalized log-logistic families of lifetime distributions. Journal of Probability and Statistical Science, 4, (2006), 51-64.
  • Gupta R.C and Gupta R.D., Generalized skew normal model. Test 13, (2004), 501-524.
  • Haghbin, H., Ozel, G., Alizadeh, M. and Hamedani, G. G., A new generalized odd log-logistic family of distributions. Communications in Statistics-Theory and Methods, 46, (2017), 9897-9920.
  • Hamedani, G.G., On certain generalized gamma convolution distributions II, Technical Report No. 484, MSCS, Marquette University (2013).
  • Jamalizadeh, A., Arabpour, A. R. and Balakrishnan, N., A generalized skew two-piece skew-normal distribution. Statistical Papers, 52, (2011), 431-446.
  • Korkmaz, M. Ç., Yousof, H. M. and Hamedani G. G., The exponential Lindley odd log-logistic G family: properties, characterizations and applications. Journal of Statistical Theory and Applications, 17, (2018), 554-571.
  • Kotz, S. and Seier, E., Kurtosis of the Topp Leone distributions. Interstat, (2007, )1-15.
  • Marshall, A. W. and Olkin, I., A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, (1997), 641-652.
  • Meeker, W.Q. and Escobar, L.A., Statistical Methods for Reliability Data. John Wiley, New York (1998).
  • Mudholkar, G. S. and Srivastava, D. K., Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42, (1993), 299-302.
  • Nadarajah, S., Kotz, S., Moments of some J-shaped distributions. Journal of Applied Statistics, 30, (2003), 311-317.
  • Roberts, H. V., Data analysis for managers with minitab. Scientific Press, Redwood City, (1988).
  • Sharafi M. and Behboodian J., The Balakrishnan skew-normal density. Statistical Papers 49, (2008), 769-778
  • Zghoul, A. A., Record values from a family of J-shaped distributions. Statistica, 71, (2011), 355-365.
  • Zhou, M., Yang, D. W., Wang, Y., Nadarajah, S., Some J-shaped distributions: Sums, products and ratios. In Proceedings of the Annual Reliability and Maintainability Symposium, pp. 175-181, (2006).

The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications

Year 2019, Volume: 68 Issue: 2, 1506 - 1527, 01.08.2019
https://doi.org/10.31801/cfsuasmas.542988

Abstract

A new family of distributions called the Topp-Leone generalized odd log-logistic-G family is introduced and studied. We provide some mathematical properties of the new family including ordinary and incomplete moments, generating function and order statistics. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. Finally, the usefulness of the family is illustrated by means of two real data sets. The new model provides consistently better fits than other competitive models for these data sets.

References

  • Aarset, M. V., How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36, (1987), 106-108.
  • Alexander, C., Cordeiro, G. M., Ortega, E. M. and Sarabia, J. M., Generalized beta-generated distributions. Computational Statistics and Data Analysis, 56(6), (2012), 1880-1897.
  • Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G.M., Ortega, E.M.M. and Pescim, R.R., The Kumaraswamy odd log-logistic family of distributions, Hacettepe Journal of Mathematics and Statistics, 44, (2015), 1491-1512.
  • 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, (2016a), 1781-1803.
  • Cordeiro, G.M., Alizadeh, M., Tahir, M. H., Mansoor, M., Bourguignon, M. and Hamedani G.G., The beta dd log-logistic generalized family of distributions, Hacettepe Journal of Mathematics and Statistics, 45, (2016b), 1175-1202.
  • Cordeiro, G.M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E.M.M. and Altun, E., The generalized odd log-logistic family of distributions: properties, regression models and applications, Journal of Statistical Computation and Simulation, 87, (2017), 908-932.
  • Braga, A.S., Cordeiro, G. M., Ortega, E. M. and Nilton da Cruz, J., The odd log-logistic normal distribution: Theory and applications in analysis of experiments. Journal of Statistical Theory and Practice, 10(2), (2016), 311-335.
  • Brito, E., Cordeiro, G. M., Yousof, H. M., Alizadeh, M.and Silva, G. O., The Topp-Leone odd log-logistic family of distributions. Journal of Statistical Computation and Simulation, 87, (2017), 3040-3058.
  • Chen, G. and Balakrishnan, N., A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27, (1995) 154-161.
  • Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E. M. M. and Altun, E., The generalized odd log-logistic family of distributions: properties, regression models and applications. Journal of Statistical Computation and Simulation, 87, (2017), 908-932.
  • Cordeiro, G. M. and de Castro, M., A new family of generalized distributions. Journal of statistical computation and simulation, 81, (2011), 883-898.
  • Cordeiro, G. M., Ortega, E. M. and Nadarajah, S., The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347, (2010), 1399-1429.
  • Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31, (2002), 497-512.
  • Evans, D. L., Drew, J. H. and Leemis, L. M., The distribution of the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling test statistics for exponential populations with estimated parameters. Communications in Statistics-Simulation and Computation, 37, (2008) 1396-1421.
  • Famoye, F., Lee, C. and Olumolade, O., The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4, (2005), 121-136.
  • Garcia, V. J., Gomez-Deniz, E. and Vazquez-Polo, F. J., A new skew generalization of the normal distribution: Properties and applications. Computational Statistics & Data Analysis, 54(8), (2010), 2021-2034.
  • Genç, A., Moments of order statistics of Topp Leone distribution. Statistical Papers, 51, (2012) , 1-15.
  • Genç, A., Estimation of the Prob(X > Y) with Topp Leone distribution. Journal of Statistical Computation and Simulation, 83, (2013), 326-339.
  • Ghitany, M. E., Kotz, S., Xie, M., On some reliability measures and their stochastic orderings for the Topp Leone distribution. Journal of Applied Statistics, 32, (2005), 715-722.
  • Glänzel, 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, (1987), 75--84.
  • Glänzel, W., Some consequences of a characterization theorem based on truncated moments. Statistics: A Journal of Theoretical and Applied Statistics, 21, (1990), 613-618.
  • Gleaton, J. U. and Lynch, J. D., Properties of generalized log-logistic families of lifetime distributions. Journal of Probability and Statistical Science, 4, (2006), 51-64.
  • Gupta R.C and Gupta R.D., Generalized skew normal model. Test 13, (2004), 501-524.
  • Haghbin, H., Ozel, G., Alizadeh, M. and Hamedani, G. G., A new generalized odd log-logistic family of distributions. Communications in Statistics-Theory and Methods, 46, (2017), 9897-9920.
  • Hamedani, G.G., On certain generalized gamma convolution distributions II, Technical Report No. 484, MSCS, Marquette University (2013).
  • Jamalizadeh, A., Arabpour, A. R. and Balakrishnan, N., A generalized skew two-piece skew-normal distribution. Statistical Papers, 52, (2011), 431-446.
  • Korkmaz, M. Ç., Yousof, H. M. and Hamedani G. G., The exponential Lindley odd log-logistic G family: properties, characterizations and applications. Journal of Statistical Theory and Applications, 17, (2018), 554-571.
  • Kotz, S. and Seier, E., Kurtosis of the Topp Leone distributions. Interstat, (2007, )1-15.
  • Marshall, A. W. and Olkin, I., A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, (1997), 641-652.
  • Meeker, W.Q. and Escobar, L.A., Statistical Methods for Reliability Data. John Wiley, New York (1998).
  • Mudholkar, G. S. and Srivastava, D. K., Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42, (1993), 299-302.
  • Nadarajah, S., Kotz, S., Moments of some J-shaped distributions. Journal of Applied Statistics, 30, (2003), 311-317.
  • Roberts, H. V., Data analysis for managers with minitab. Scientific Press, Redwood City, (1988).
  • Sharafi M. and Behboodian J., The Balakrishnan skew-normal density. Statistical Papers 49, (2008), 769-778
  • Zghoul, A. A., Record values from a family of J-shaped distributions. Statistica, 71, (2011), 355-365.
  • Zhou, M., Yang, D. W., Wang, Y., Nadarajah, S., Some J-shaped distributions: Sums, products and ratios. In Proceedings of the Annual Reliability and Maintainability Symposium, pp. 175-181, (2006).
There are 36 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

M. Ç. Korkmaz 0000-0003-3302-0705

H. M. Yousof 0000-0003-4589-4944

M. Alizadeh 0000-0001-6638-2185

G.g. Hamedani 0000-0001-7976-1088

Publication Date August 1, 2019
Submission Date October 5, 2017
Acceptance Date November 11, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Korkmaz, M. Ç., Yousof, H. M., Alizadeh, M., Hamedani, G. (2019). The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1506-1527. https://doi.org/10.31801/cfsuasmas.542988
AMA Korkmaz MÇ, Yousof HM, Alizadeh M, Hamedani G. The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1506-1527. doi:10.31801/cfsuasmas.542988
Chicago Korkmaz, M. Ç., H. M. Yousof, M. Alizadeh, and G.g. Hamedani. “The Topp-Leone Generalized Odd Log-Logistic Family of Distributions: Properties, Characterizations and Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1506-27. https://doi.org/10.31801/cfsuasmas.542988.
EndNote Korkmaz MÇ, Yousof HM, Alizadeh M, Hamedani G (August 1, 2019) The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1506–1527.
IEEE M. Ç. Korkmaz, H. M. Yousof, M. Alizadeh, and G. Hamedani, “The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1506–1527, 2019, doi: 10.31801/cfsuasmas.542988.
ISNAD Korkmaz, M. Ç. et al. “The Topp-Leone Generalized Odd Log-Logistic Family of Distributions: Properties, Characterizations and Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1506-1527. https://doi.org/10.31801/cfsuasmas.542988.
JAMA Korkmaz MÇ, Yousof HM, Alizadeh M, Hamedani G. The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1506–1527.
MLA Korkmaz, M. Ç. et al. “The Topp-Leone Generalized Odd Log-Logistic Family of Distributions: Properties, Characterizations and Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1506-27, doi:10.31801/cfsuasmas.542988.
Vancouver Korkmaz MÇ, Yousof HM, Alizadeh M, Hamedani G. The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1506-27.

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