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Year 2020, Volume: 69 Issue: 1, 137 - 157, 30.06.2020

Monireh Hameldarbandi Mehmet Yılmaz

https://doi.org/10.31801/cfsuasmas.567496
Cited By: 1

Abstract

References

  • Abd El Hady, N. E., Exponentiated Transmuted Weibull Distribution, International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering, 8(6) (2014).
  • Akinsete, A., Famoye, F. and Lee, C., The Beta-Pareto distribution, Statistics, 42(6) (2008) 547--563.
  • Al-Mutairi, D. K., Ghitany, M. E., and Kundu, D., Inferences on stress-strength reliability from Lindley distributions, Communications in Statistics-Theory and Methods, 42 (8), (2013), 1443--1463.
  • Aryal, G. R. and Tsokos, C. P., On the transmuted extreme value distribution with application, Nonlinear Analysis: Theory, Methods & Applications, 71(12) (2009), 1401--1407.
  • Aryal, G. R. and Tsokos, C. P., Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution, European Journal of Pure and Applied Mathematics, 4(2) (2011), 89--102.
  • Aryal, G. R., Transmuted log-logistic distribution, Journal of Statistics Applications & Probability, 2(1) (2013), 11-20.
  • Ashour, S. K. and Eltehiwy, M. A., Transmuted Lomax distribution, American Journal of Applied Mathematics and Statistics, 1(6) (2013a), 121--127.
  • Ashour, S. K. and Eltehiwy, M. A., Transmuted exponentiated Lomax distribution, Aust J Basic Appl Sci, 7(7) (2013b), 658--667.
  • Bourguignon, M., Silva, R. B., Zea, L. M. and Cordeiro, G. M., The Kumaraswamy Pareto distribution, Journal of Statistical Theory and Applications, 12(2) (2013), 129--144.
  • Choulakian, V. and Stephens, M. A., Goodness-of-fit tests for the generalized Pareto distribution, Technometrics, 43(4) (2001), 478--484.
  • Elbatal, I., Asha, G. and Raja, V., Transmuted exponentiated Fréchet distribution: properties and applications, J. Stat. Appl. Prob, 3 (2014), 379--394.
  • Elbatal, I. and Aryal, G., On the Transmuted Additive Weibull Distribution, Austrian Journal of Statistics, 42(2) (2016), 117--132.
  • Eltehiwy, M. and Ashour, S., Transmuted exponentiated modified Weibull distribution, International Journal of Basic and Applied Sciences, 2(3) (2013), 258--269.
  • Gentle, J. E., Random number generation and Monte Carlo methods, Springer Science & Business Media, 2013.
  • Gumbel, E.J., Bivariate Exponential Distributions, Journal of the American Statistical Association, 55(292) (1960), 698--707.
  • Hussian, M. A., Transmuted exponentiated gamma distribution: A generalization of the exponentiated gamma probability distribution, Applied Mathematical Sciences, 8(27) (2014), 1297--1310.
  • Johnson, N. L. and Kotz, S., A vector multivariate hazard rate, Journal of Multivariate Analysis, 5(1) (1975), 53--66.
  • Lee, E. T. and Wang, J., Statistical methods for survival data analysis, John Wiley & Sons Vol. 476, 2003.
  • Merovci, F., Transmuted Lindley distribution, International Journal of Open Problems in Computer Science and Mathematics, 6, (2013a).
  • Merovci, F., Transmuted exponentiated exponential distribution, Mathematical Sciences and Applications E-Notes, 1(2) (2013b).
  • Merovci, F. and Elbatal, I., Transmuted Lindley-geometric distribution and its applications, arXiv preprint arXiv:1309, 3774, (2013).
  • Merovci, F. and Puka, L., Transmuted pareto distribution, In ProbStat Forum, Vol. 7 (2014), 1--11. Merovci2016 : Merovci, F., Transmuted Rayleigh distribution, Austrian Journal of Statistics, 42(1) (2016), 21--31.
  • Nasiru, S. and Luguterah, A., The new Weibull-Pareto distribution, Pakistan Journal of Statistics and Operation Research, 11(1), (2015).
  • Rényi, A., On measures of entropy and information, In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, (Vol. 1) (1961), 547--561.
  • Shaked, M. and Shanthikumar, J. G., Multivariate conditional hazard rate functions--an overview, Applied Stochastic Models in Business and Industry, 31(3) (2015), 285--296.
  • Shaw, W. T. and Buckley, I. R., The alchemy of probability distributions: Beyond gram-charlier and cornish-fisher expansions, and skew-normal or kurtotic-normal distributions, Submitted, Feb, 7, 64, 2007.
  • Shaw, W. T. and Buckley, I. R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv preprint arXiv:0901.0434, 2009.
  • Singh, S. K., Singh, U., and Sharma, V. K., Estimation on System Reliability in Generalized Lindley Stress-Strength Model, J. Stat. Appl. Prob, 3, (2014), 61--75.
  • Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M. and Zubair, M., A New Weibull--Pareto Properties and Applications, Communications in Statistics-Simulation and Computation, 45(10) (2016), 3548--3567.
  • Yilmaz, M., Hameldarbandi, M. and Kemaloglu, S. A., Exponential-modified discrete Lindley distribution, SpringerPlus, 5(1) (2016), 1660.

Transmuted Gumbel univariate exponential distribution

Year 2020, Volume: 69 Issue: 1, 137 - 157, 30.06.2020

Monireh Hameldarbandi Mehmet Yılmaz

https://doi.org/10.31801/cfsuasmas.567496
Cited By: 1

Abstract

A functional composition of the distribution function of one probability distribution with the inverse distribution function of another is called the transmutation map. The present paper is purported to show how the transmuted distribution can be obtained by using the convex combination of failure probability of two-component systems. The transmuted Gumbel univariate exponential distribution is presented by changing convex combination parameter. This new distribution is dened and studied. Some mathematical properties of this distribution including the generating function and ordinary moments are derived. The survival, hazard rate and mean residual life functions are discussed. Finally, three applications to real data are presented.

Keywords

Gumbel exponential distribution convex combination transmutation method hazard rate function Exponential Distribution

References

  • Abd El Hady, N. E., Exponentiated Transmuted Weibull Distribution, International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering, 8(6) (2014).
  • Akinsete, A., Famoye, F. and Lee, C., The Beta-Pareto distribution, Statistics, 42(6) (2008) 547--563.
  • Al-Mutairi, D. K., Ghitany, M. E., and Kundu, D., Inferences on stress-strength reliability from Lindley distributions, Communications in Statistics-Theory and Methods, 42 (8), (2013), 1443--1463.
  • Aryal, G. R. and Tsokos, C. P., On the transmuted extreme value distribution with application, Nonlinear Analysis: Theory, Methods & Applications, 71(12) (2009), 1401--1407.
  • Aryal, G. R. and Tsokos, C. P., Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution, European Journal of Pure and Applied Mathematics, 4(2) (2011), 89--102.
  • Aryal, G. R., Transmuted log-logistic distribution, Journal of Statistics Applications & Probability, 2(1) (2013), 11-20.
  • Ashour, S. K. and Eltehiwy, M. A., Transmuted Lomax distribution, American Journal of Applied Mathematics and Statistics, 1(6) (2013a), 121--127.
  • Ashour, S. K. and Eltehiwy, M. A., Transmuted exponentiated Lomax distribution, Aust J Basic Appl Sci, 7(7) (2013b), 658--667.
  • Bourguignon, M., Silva, R. B., Zea, L. M. and Cordeiro, G. M., The Kumaraswamy Pareto distribution, Journal of Statistical Theory and Applications, 12(2) (2013), 129--144.
  • Choulakian, V. and Stephens, M. A., Goodness-of-fit tests for the generalized Pareto distribution, Technometrics, 43(4) (2001), 478--484.
  • Elbatal, I., Asha, G. and Raja, V., Transmuted exponentiated Fréchet distribution: properties and applications, J. Stat. Appl. Prob, 3 (2014), 379--394.
  • Elbatal, I. and Aryal, G., On the Transmuted Additive Weibull Distribution, Austrian Journal of Statistics, 42(2) (2016), 117--132.
  • Eltehiwy, M. and Ashour, S., Transmuted exponentiated modified Weibull distribution, International Journal of Basic and Applied Sciences, 2(3) (2013), 258--269.
  • Gentle, J. E., Random number generation and Monte Carlo methods, Springer Science & Business Media, 2013.
  • Gumbel, E.J., Bivariate Exponential Distributions, Journal of the American Statistical Association, 55(292) (1960), 698--707.
  • Hussian, M. A., Transmuted exponentiated gamma distribution: A generalization of the exponentiated gamma probability distribution, Applied Mathematical Sciences, 8(27) (2014), 1297--1310.
  • Johnson, N. L. and Kotz, S., A vector multivariate hazard rate, Journal of Multivariate Analysis, 5(1) (1975), 53--66.
  • Lee, E. T. and Wang, J., Statistical methods for survival data analysis, John Wiley & Sons Vol. 476, 2003.
  • Merovci, F., Transmuted Lindley distribution, International Journal of Open Problems in Computer Science and Mathematics, 6, (2013a).
  • Merovci, F., Transmuted exponentiated exponential distribution, Mathematical Sciences and Applications E-Notes, 1(2) (2013b).
  • Merovci, F. and Elbatal, I., Transmuted Lindley-geometric distribution and its applications, arXiv preprint arXiv:1309, 3774, (2013).
  • Merovci, F. and Puka, L., Transmuted pareto distribution, In ProbStat Forum, Vol. 7 (2014), 1--11. Merovci2016 : Merovci, F., Transmuted Rayleigh distribution, Austrian Journal of Statistics, 42(1) (2016), 21--31.
  • Nasiru, S. and Luguterah, A., The new Weibull-Pareto distribution, Pakistan Journal of Statistics and Operation Research, 11(1), (2015).
  • Rényi, A., On measures of entropy and information, In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, (Vol. 1) (1961), 547--561.
  • Shaked, M. and Shanthikumar, J. G., Multivariate conditional hazard rate functions--an overview, Applied Stochastic Models in Business and Industry, 31(3) (2015), 285--296.
  • Shaw, W. T. and Buckley, I. R., The alchemy of probability distributions: Beyond gram-charlier and cornish-fisher expansions, and skew-normal or kurtotic-normal distributions, Submitted, Feb, 7, 64, 2007.
  • Shaw, W. T. and Buckley, I. R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv preprint arXiv:0901.0434, 2009.
  • Singh, S. K., Singh, U., and Sharma, V. K., Estimation on System Reliability in Generalized Lindley Stress-Strength Model, J. Stat. Appl. Prob, 3, (2014), 61--75.
  • Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M. and Zubair, M., A New Weibull--Pareto Properties and Applications, Communications in Statistics-Simulation and Computation, 45(10) (2016), 3548--3567.
  • Yilmaz, M., Hameldarbandi, M. and Kemaloglu, S. A., Exponential-modified discrete Lindley distribution, SpringerPlus, 5(1) (2016), 1660.
There are 30 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Monireh Hameldarbandi 0000-0002-3543-3709

Mehmet Yılmaz 0000-0002-9762-6688

Publication Date June 30, 2020
Submission Date May 19, 2019
Acceptance Date September 2, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Hameldarbandi, M., & Yılmaz, M. (2020). Transmuted Gumbel univariate exponential distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 137-157. https://doi.org/10.31801/cfsuasmas.567496
AMA Hameldarbandi M, Yılmaz M. Transmuted Gumbel univariate exponential distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):137-157. doi:10.31801/cfsuasmas.567496
Chicago Hameldarbandi, Monireh, and Mehmet Yılmaz. “Transmuted Gumbel Univariate Exponential Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 137-57. https://doi.org/10.31801/cfsuasmas.567496.
EndNote Hameldarbandi M, Yılmaz M (June 1, 2020) Transmuted Gumbel univariate exponential distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 137–157.
IEEE M. Hameldarbandi and M. Yılmaz, “Transmuted Gumbel univariate exponential distribution”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 137–157, 2020, doi: 10.31801/cfsuasmas.567496.
ISNAD Hameldarbandi, Monireh - Yılmaz, Mehmet. “Transmuted Gumbel Univariate Exponential Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 137-157. https://doi.org/10.31801/cfsuasmas.567496.
JAMA Hameldarbandi M, Yılmaz M. Transmuted Gumbel univariate exponential distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:137–157.
MLA Hameldarbandi, Monireh and Mehmet Yılmaz. “Transmuted Gumbel Univariate Exponential Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 137-5, doi:10.31801/cfsuasmas.567496.
Vancouver Hameldarbandi M, Yılmaz M. Transmuted Gumbel univariate exponential distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):137-5.

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