A new lifetime distribution: transmuted exponential power distribution

Buğra Saraçoğlu; Caner Tanış

doi:10.31801/cfsuasmas.528306

Research Article

A new lifetime distribution: transmuted exponential power distribution

Year 2021, Volume: 70 Issue: 1, 1 - 14, 30.06.2021

Buğra Saraçoğlu Caner Tanış

https://doi.org/10.31801/cfsuasmas.528306

Cited By: 5

Abstract

In this study, a new statistical distribution called as Transmuted Exponential Power distribution using the quadratic rank transmutation map introduced by Shaw and Buckley [23,24] is suggested. The various mathematical and statistical properties of this distribution are examined. The method of maximum likelihood estimation has been used to estimate the unknown parameters of this distribution. Moreover, real data analysis is used to compare this new distribution with other some distributions using some goodness of fit measures.

Keywords

Transmuted exponential power distribution, Quadratic rank transmu- tation map, Maximum likelihood estimation

References

Akdam, N., Kinaci, I., Saracoğlu, B., Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples, Hacettepe Journal of Mathematics and Statistics, 46 (2017), 239-253.
Al-Babtain, A., Fattah, A. A., Ahmed, A. H. N., Merovci, F., The Kumaraswamy-transmuted exponentiated modified Weibull distribution, Communications in Statistics-Simulation and Computation, 46 (2017), 3812-3832.
Aryal, G. R., Tsokos, C. P., Transmuted Weibull distribution: A generalization of the Weibull probability distribution, European Journal of Pure and Applied Mathematics 4 (2011), 89-102.
Aryal, G. R., Tsokos, C. P., On the transmuted extreme value distribution with application, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), 1401-1407.
Ashour, S. K., Eltehiwy, M. A., Transmuted exponentiated Lomax distribution, Aust J Basic Appl Sci, 7 (2013), 658-667.
Ashour, S. K., Eltehiwy, M. A., Transmuted lomax distribution, American Journal of Applied Mathematics and Statistics, 1 (2013), 121-127.
Barriga, G. D., Louzada-Neto, F., Cancho, V. G. The complementary exponential power lifetime model, Computational statistics and data analysis, 55(3) (2011), 1250-1259.
Chen Z. Statistical inference about the shape parameter of the exponential power distribution.Statistical Papers, 40(1) (1999), 459-468.
Dasgupta, R., On the distribution of burr with applications, Sankhya B, 73 (2011), 1-19.
Elbatal, I., Aryal, G., On the Transmuted Additive Weibull Distribution, Austrian Journal of Statistics, 42 (2016), 117-132.
El-Gohary, A., Alshamrani, A., Al-Otaibi, A. N., The generalized Gompertz distribution, Applied Mathematical Modelling, 37 (1-2) (2013), 13-24.
Gupta, R. D., Kundu, D., Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical journal, 43 (2001), 117-130.
Hussian, M. A., Transmuted exponentiated gamma distribution: A generalization of the exponentiated gamma probability distribution, Applied Mathematical Sciences, 8 (2014), 1297-1310.
Khan, M S., King, R. and Hudson, I L., Transmuted Kumaraswamy Distribution. Statistics in Transition new series, 17 (2016), 183-210.
Khan, M. S., King, R. and & Hudson, I L., Transmuted Weibull distribution: Properties and estimation, Communications in Statistics-Theory and Methods, 46 (2017), 5394-5418.
Khan, M. S., King, R. and Hudson, I L., Transmuted generalized Gompertz distribution with application, Journal of Statistical Theory and Applications, 16 (2017), 65-80.
Mahmoud, M. R. and & Mandouh, R M. On the transmuted Fréchet distribution, Journal of Applied Sciences Research, 9 (2013), 5553-5561.
Merovci, F., Transmuted rayleigh distribution, Austrian Journal of Statistics, 42 (2013), 21-31.
Merovci, F., Transmuted generalized Rayleigh distribution, Journal of Statistics Applications & Probability, 3 (2014), 9-20.
Merovci, F., Transmuted lindley distribution, International Journal of Open Problems in Computer Science and Mathematics, 6 (2014), 63-72.
Merovci, F., Transmuted exponentiated exponential distribution, Mathematical Sciences and Applications ENotes, 1 (2013) 112-122.
Nichols, M. D., Padgett W. J., A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International,, 22 (2006) 141--151.
Smith, R.M., Bain, L.J., An exponential power life-testing distribution, Communications in Statistics,, 4(5) (1975), 469-481.
Shahzad, M. N., Asghar, Z., Transmuted Dagum distribution: A more flexible and broad shaped hazard function model, Hacettepe Journal of Mathematics and Statistics, 45 (2016), 227-244.
Shaw, W. T. , Buckley, I. R., The Alchemy of Probability Distributions: Beyond Gram Charlier & Cornish Fisher Expansions, and Skew-Normal or Kurtotic-Normal Distributions, Technical report, Financial Mathematics Group, King's College, London, U.K. 2007.
Shaw, W. T., Buckley, I. R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skewkurtotic-normal distribution from a rank transmutation map, arXiv preprint (2009) arXiv:0901.0434.
Yousof, H. M., Alizadeh, M., Jahanshahi, S. M. A., Ramiresd, T. G., Ghoshe, I., Hamedani, G. G., The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, Journal of Data Science, 15 (2017), 723-740.

Year 2021, Volume: 70 Issue: 1, 1 - 14, 30.06.2021

Buğra Saraçoğlu Caner Tanış

https://doi.org/10.31801/cfsuasmas.528306

Cited By: 5

Abstract

References

Akdam, N., Kinaci, I., Saracoğlu, B., Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples, Hacettepe Journal of Mathematics and Statistics, 46 (2017), 239-253.
Al-Babtain, A., Fattah, A. A., Ahmed, A. H. N., Merovci, F., The Kumaraswamy-transmuted exponentiated modified Weibull distribution, Communications in Statistics-Simulation and Computation, 46 (2017), 3812-3832.
Aryal, G. R., Tsokos, C. P., Transmuted Weibull distribution: A generalization of the Weibull probability distribution, European Journal of Pure and Applied Mathematics 4 (2011), 89-102.
Aryal, G. R., Tsokos, C. P., On the transmuted extreme value distribution with application, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), 1401-1407.
Ashour, S. K., Eltehiwy, M. A., Transmuted exponentiated Lomax distribution, Aust J Basic Appl Sci, 7 (2013), 658-667.
Ashour, S. K., Eltehiwy, M. A., Transmuted lomax distribution, American Journal of Applied Mathematics and Statistics, 1 (2013), 121-127.
Barriga, G. D., Louzada-Neto, F., Cancho, V. G. The complementary exponential power lifetime model, Computational statistics and data analysis, 55(3) (2011), 1250-1259.
Chen Z. Statistical inference about the shape parameter of the exponential power distribution.Statistical Papers, 40(1) (1999), 459-468.
Dasgupta, R., On the distribution of burr with applications, Sankhya B, 73 (2011), 1-19.
Elbatal, I., Aryal, G., On the Transmuted Additive Weibull Distribution, Austrian Journal of Statistics, 42 (2016), 117-132.
El-Gohary, A., Alshamrani, A., Al-Otaibi, A. N., The generalized Gompertz distribution, Applied Mathematical Modelling, 37 (1-2) (2013), 13-24.
Gupta, R. D., Kundu, D., Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical journal, 43 (2001), 117-130.
Hussian, M. A., Transmuted exponentiated gamma distribution: A generalization of the exponentiated gamma probability distribution, Applied Mathematical Sciences, 8 (2014), 1297-1310.
Khan, M S., King, R. and Hudson, I L., Transmuted Kumaraswamy Distribution. Statistics in Transition new series, 17 (2016), 183-210.
Khan, M. S., King, R. and & Hudson, I L., Transmuted Weibull distribution: Properties and estimation, Communications in Statistics-Theory and Methods, 46 (2017), 5394-5418.
Khan, M. S., King, R. and Hudson, I L., Transmuted generalized Gompertz distribution with application, Journal of Statistical Theory and Applications, 16 (2017), 65-80.
Mahmoud, M. R. and & Mandouh, R M. On the transmuted Fréchet distribution, Journal of Applied Sciences Research, 9 (2013), 5553-5561.
Merovci, F., Transmuted rayleigh distribution, Austrian Journal of Statistics, 42 (2013), 21-31.
Merovci, F., Transmuted generalized Rayleigh distribution, Journal of Statistics Applications & Probability, 3 (2014), 9-20.
Merovci, F., Transmuted lindley distribution, International Journal of Open Problems in Computer Science and Mathematics, 6 (2014), 63-72.
Merovci, F., Transmuted exponentiated exponential distribution, Mathematical Sciences and Applications ENotes, 1 (2013) 112-122.
Nichols, M. D., Padgett W. J., A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International,, 22 (2006) 141--151.
Smith, R.M., Bain, L.J., An exponential power life-testing distribution, Communications in Statistics,, 4(5) (1975), 469-481.
Shahzad, M. N., Asghar, Z., Transmuted Dagum distribution: A more flexible and broad shaped hazard function model, Hacettepe Journal of Mathematics and Statistics, 45 (2016), 227-244.
Shaw, W. T. , Buckley, I. R., The Alchemy of Probability Distributions: Beyond Gram Charlier & Cornish Fisher Expansions, and Skew-Normal or Kurtotic-Normal Distributions, Technical report, Financial Mathematics Group, King's College, London, U.K. 2007.
Shaw, W. T., Buckley, I. R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skewkurtotic-normal distribution from a rank transmutation map, arXiv preprint (2009) arXiv:0901.0434.
Yousof, H. M., Alizadeh, M., Jahanshahi, S. M. A., Ramiresd, T. G., Ghoshe, I., Hamedani, G. G., The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, Journal of Data Science, 15 (2017), 723-740.

There are 27 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Buğra Saraçoğlu 0000-0003-1713-2862 Caner Tanış 0000-0003-0090-1661
Publication Date	June 30, 2021
Submission Date	February 18, 2019
Acceptance Date	October 26, 2020
Published in Issue	Year 2021 Volume: 70 Issue: 1

Cite

APA	Saraçoğlu, B., & Tanış, C. (2021). A new lifetime distribution: transmuted exponential power distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 1-14. https://doi.org/10.31801/cfsuasmas.528306
AMA	Saraçoğlu B, Tanış C. A new lifetime distribution: transmuted exponential power distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):1-14. doi:10.31801/cfsuasmas.528306
Chicago	Saraçoğlu, Buğra, and Caner Tanış. “A New Lifetime Distribution: Transmuted Exponential Power Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 1-14. https://doi.org/10.31801/cfsuasmas.528306.
EndNote	Saraçoğlu B, Tanış C (June 1, 2021) A new lifetime distribution: transmuted exponential power distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 1–14.
IEEE	B. Saraçoğlu and C. Tanış, “A new lifetime distribution: transmuted exponential power distribution”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 1–14, 2021, doi: 10.31801/cfsuasmas.528306.
ISNAD	Saraçoğlu, Buğra - Tanış, Caner. “A New Lifetime Distribution: Transmuted Exponential Power Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 1-14. https://doi.org/10.31801/cfsuasmas.528306.
JAMA	Saraçoğlu B, Tanış C. A new lifetime distribution: transmuted exponential power distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:1–14.
MLA	Saraçoğlu, Buğra and Caner Tanış. “A New Lifetime Distribution: Transmuted Exponential Power Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 1-14, doi:10.31801/cfsuasmas.528306.
Vancouver	Saraçoğlu B, Tanış C. A new lifetime distribution: transmuted exponential power distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):1-14.