Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications
Yıl 2019,
Cilt: 12 Sayı: 1, 35 - 48, 31.07.2019
Joseph Thomas
Samuel Chiabom Zelibe
Eferhonore Eyefia
Öz
This study introduced a new distribution from the alpha power inverted exponential family of distributions
called Kumaraswamy Alpha Power Inverted Exponential distribution (KAPIE). We provide some of the statistical properties of this distribution; such as hazard rate function, quantile function, skewness, kurtosis, and order statistics.
The parameters of the distribution are obtained by a method of maximum likelihood approach. The empirical importance
and flexibility of this new distribution in modeling with real-life dataset applications was carefully examined and competes favourably well with other distributions.
Kaynakça
- Abouammoh, A.M., and Alshingiti, A.M. (2009). Reliability estimation of generalized inverted exponential distribution. Journal of Statistical Computation and Simulation, 79(11), 1301--1315.
- Anake, T. A., Oguntunde, P. E., and Odetunmibi, O. A. (2015). On a Fractional Beta-Exponential Distribution. International Journal of Mathematics and Computations, 26(1), 26-34
- Aryal, G. R. and Yousof, H. M. (2017). The exponentiated generalized-G Poisson family of distributions. Economic Quality Control, 32(1), 1-17.
- Barreto-Souza, W., and Simas, A.B. (2013). The exp-G family of probability distributions. Brazilian Journal of Probability and Statistics 27:84-109.
- Bourguignon M., Silva R. B., and Cordeiro G. M. (2014). The Weibull-G Family of Probability Distributions, Journal of Data Science, 12, 53-68.
- Cordeiro, G. M., Ortega, E. M. and da Cunha, D. C. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11, 1-27.
- Cordeiro, G.M., Hashimoto, E. M. and Ortega, E. M. M. (2014). The McDonald Weibull model. Statistics: A Journal of Theoretical and Applied Statistics, 48, 256-278.
- Cordeiro, G.M., Ortega, E. M. M. and Nadarajah, S. (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347, 1317-1336.
- Cordeiro G. M., de Castro M. (2011). A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81(7), 883-898
- Dey, S., Alzaatreh, A., Zhang, C., and Kumar, D. (2017) A new extension of generalized exponential distribution with application to ozone data. Ozone: Science and Engineering, 39(4), 273--285.
- Gupta, R. C, Gupta, P. I. and Gupta, R. D. (1998). Modeling failure time data by Lehmann alternatives. Communications in Statistics-Theory and Methods, 27, 887-904.
- Gupta, R. D., and Kundu, D. (1999). Generalized exponential distribution. Australian and New Zealand Journal of Statistics, 41 (2), 173-188.
- Haq, M. A., Butt, N. S., Usman, R. M., and Fattah, A. A. (2016). Transmuted Power Function Distribution. Gazi University Journal of Science 29(1), 177–185.
- Keller, A. Z., Kamath, A. R. R., and Perera, U. D., (1982). Reliability analysis of CNC machine tools. Reliability Engineering, 3(6): 449--473.
- Lin, C.T., Duran, B.S., and Lewis, T.O., (1989) Inverted gamma as a life distribution. Microelectronics Reliability, 29(4), 619—626
- Mahdavi, A., and Kundu, D. (2017). A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Methods, 46(13), 6543--6557.
- Merovci, F., Khaleel ,M. A., Ibrahim, N. A., and Shitan, M. (2016) The beta type X distribution: properties with application, Springer-Plus, (5), 697.
- Nadarajah, S. and Okorie I. E. (2017). On the moments of the alpha, power transformed generalized exponential distribution. The Ozone: Science and Engineering, 1--6. DOI/10.1080/01919512.2017.1419123
- Nadarajah, S., Nassiri, V., and Mohammadpour, A. (2014). Truncated-exponential skewsymmetric distributions. Statistics 48:872-895.
- Nassar, M., Alzaatreh, A., Mead, M., and Abo-Kasem, O. (2017). Alpha power Weibull distribution: properties and applications. Communications in Statistics-Theory and Methods 46:10236-10252.
- Nofal, Z. M., Afify, A. Z., Yousof, H. M. and Cordeiro, G. M. (2017). The generalized transmuted-G family of distributions. Communications in Statistics-Theory and Methods, 46, 4119-4136.
- Oguntunde, P. E., Odetunmibi, O. A., and Adejumo, A. O. (2013). On Sum of Exponentialially Distributed Random Variables: A Convolution Approach. European Journal of Statistics and Probability, 1(2). 1--8.
- Oguntunde, P.E., Babatunde, O.S., and Ogunmola, A.O., (2014a). Theoretical Analysis of the Kumaraswamy-inverse Exponential Distribution, International Journal of Statistics and Applications, 4(2), 113--116.
- Oguntunde, P.E., Adejumo, A., and Balogun, O.S. (2014b). Statistical Properties of the Exponentiated Generalized Inverted Exponential Distribution, Applied Mathematics, 4(2), 47--55.
- Oguntunde, P., and Adejumo, O. (2014c). The Transmuted Inverse Exponential Distribution. International Journal of Advanced Statistics and Probability, 3(1), 1--7.
- Oguntunde, P.E., (2017a). Generalisation of the Inverse Exponential Distribution: Statistical Properties and Applications. Phd. Thesis, Covenant University College of Science and Technology, Ota, Ogun State, 128--142.
- Oguntunde, P., Khaleel, M. A., Ahmed, M. T., Adejumo, A. O. and Odetunmibi O. A. (2017b). A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate. Hindawi Modelling and Simulation in Engineering, 1--7. doi.org/10.1155/2017/6043169
- Rastogi, M. K. and Oguntunde, P. E. (2016). Classical and Bayes estimation of reliability characteristics of the Kumaraswamy-Inverse Exponential distribution. International Journal of System Assurance Engineering and Management. /doi.org/10.1007/s13198-018-0744-7.
- Smith, R. L. and Naylor, J. C. (1987). A comparison of maximum likelihood and bayesian estimators for the three-parameter weibull distribution, Applied Statistics, 36, 258–369.
- Unal, C.,Cakmakyapan S.,and Ozel G. (2018). Alpha Power Inverted Exponential Distribution: Properties and Application. Gazi University Journal of Science, 31(3), 954--965.
- Yousof, H. M., Afify, A. Z., Hamedani, G. G. and Aryal, G. (2017a). The Burr X generator of distributions for lifetime data. Journal of Statistical Theory and Applications, 16, 288-305.
- Yousof, H. M., Rasekhi, M., Afify, A. Z., Alizadeh, M., Ghosh, I. and Hamedani G. G. (2017b). The beta Weibull-G family of distributions: theory, characterizations and applications, Pakistan Journal of Statistics, 33, 95-116.
- Yousof, H. M., Alizadeh, M., Jahanshahiand, S. M. A., Ramires, T. G., Ghosh, I. and Hamedani G. G. (2017c). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, Journal of Data Science, 15, 723-740.
Yıl 2019,
Cilt: 12 Sayı: 1, 35 - 48, 31.07.2019
Joseph Thomas
Samuel Chiabom Zelibe
Eferhonore Eyefia
Kaynakça
- Abouammoh, A.M., and Alshingiti, A.M. (2009). Reliability estimation of generalized inverted exponential distribution. Journal of Statistical Computation and Simulation, 79(11), 1301--1315.
- Anake, T. A., Oguntunde, P. E., and Odetunmibi, O. A. (2015). On a Fractional Beta-Exponential Distribution. International Journal of Mathematics and Computations, 26(1), 26-34
- Aryal, G. R. and Yousof, H. M. (2017). The exponentiated generalized-G Poisson family of distributions. Economic Quality Control, 32(1), 1-17.
- Barreto-Souza, W., and Simas, A.B. (2013). The exp-G family of probability distributions. Brazilian Journal of Probability and Statistics 27:84-109.
- Bourguignon M., Silva R. B., and Cordeiro G. M. (2014). The Weibull-G Family of Probability Distributions, Journal of Data Science, 12, 53-68.
- Cordeiro, G. M., Ortega, E. M. and da Cunha, D. C. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11, 1-27.
- Cordeiro, G.M., Hashimoto, E. M. and Ortega, E. M. M. (2014). The McDonald Weibull model. Statistics: A Journal of Theoretical and Applied Statistics, 48, 256-278.
- Cordeiro, G.M., Ortega, E. M. M. and Nadarajah, S. (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347, 1317-1336.
- Cordeiro G. M., de Castro M. (2011). A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81(7), 883-898
- Dey, S., Alzaatreh, A., Zhang, C., and Kumar, D. (2017) A new extension of generalized exponential distribution with application to ozone data. Ozone: Science and Engineering, 39(4), 273--285.
- Gupta, R. C, Gupta, P. I. and Gupta, R. D. (1998). Modeling failure time data by Lehmann alternatives. Communications in Statistics-Theory and Methods, 27, 887-904.
- Gupta, R. D., and Kundu, D. (1999). Generalized exponential distribution. Australian and New Zealand Journal of Statistics, 41 (2), 173-188.
- Haq, M. A., Butt, N. S., Usman, R. M., and Fattah, A. A. (2016). Transmuted Power Function Distribution. Gazi University Journal of Science 29(1), 177–185.
- Keller, A. Z., Kamath, A. R. R., and Perera, U. D., (1982). Reliability analysis of CNC machine tools. Reliability Engineering, 3(6): 449--473.
- Lin, C.T., Duran, B.S., and Lewis, T.O., (1989) Inverted gamma as a life distribution. Microelectronics Reliability, 29(4), 619—626
- Mahdavi, A., and Kundu, D. (2017). A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Methods, 46(13), 6543--6557.
- Merovci, F., Khaleel ,M. A., Ibrahim, N. A., and Shitan, M. (2016) The beta type X distribution: properties with application, Springer-Plus, (5), 697.
- Nadarajah, S. and Okorie I. E. (2017). On the moments of the alpha, power transformed generalized exponential distribution. The Ozone: Science and Engineering, 1--6. DOI/10.1080/01919512.2017.1419123
- Nadarajah, S., Nassiri, V., and Mohammadpour, A. (2014). Truncated-exponential skewsymmetric distributions. Statistics 48:872-895.
- Nassar, M., Alzaatreh, A., Mead, M., and Abo-Kasem, O. (2017). Alpha power Weibull distribution: properties and applications. Communications in Statistics-Theory and Methods 46:10236-10252.
- Nofal, Z. M., Afify, A. Z., Yousof, H. M. and Cordeiro, G. M. (2017). The generalized transmuted-G family of distributions. Communications in Statistics-Theory and Methods, 46, 4119-4136.
- Oguntunde, P. E., Odetunmibi, O. A., and Adejumo, A. O. (2013). On Sum of Exponentialially Distributed Random Variables: A Convolution Approach. European Journal of Statistics and Probability, 1(2). 1--8.
- Oguntunde, P.E., Babatunde, O.S., and Ogunmola, A.O., (2014a). Theoretical Analysis of the Kumaraswamy-inverse Exponential Distribution, International Journal of Statistics and Applications, 4(2), 113--116.
- Oguntunde, P.E., Adejumo, A., and Balogun, O.S. (2014b). Statistical Properties of the Exponentiated Generalized Inverted Exponential Distribution, Applied Mathematics, 4(2), 47--55.
- Oguntunde, P., and Adejumo, O. (2014c). The Transmuted Inverse Exponential Distribution. International Journal of Advanced Statistics and Probability, 3(1), 1--7.
- Oguntunde, P.E., (2017a). Generalisation of the Inverse Exponential Distribution: Statistical Properties and Applications. Phd. Thesis, Covenant University College of Science and Technology, Ota, Ogun State, 128--142.
- Oguntunde, P., Khaleel, M. A., Ahmed, M. T., Adejumo, A. O. and Odetunmibi O. A. (2017b). A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate. Hindawi Modelling and Simulation in Engineering, 1--7. doi.org/10.1155/2017/6043169
- Rastogi, M. K. and Oguntunde, P. E. (2016). Classical and Bayes estimation of reliability characteristics of the Kumaraswamy-Inverse Exponential distribution. International Journal of System Assurance Engineering and Management. /doi.org/10.1007/s13198-018-0744-7.
- Smith, R. L. and Naylor, J. C. (1987). A comparison of maximum likelihood and bayesian estimators for the three-parameter weibull distribution, Applied Statistics, 36, 258–369.
- Unal, C.,Cakmakyapan S.,and Ozel G. (2018). Alpha Power Inverted Exponential Distribution: Properties and Application. Gazi University Journal of Science, 31(3), 954--965.
- Yousof, H. M., Afify, A. Z., Hamedani, G. G. and Aryal, G. (2017a). The Burr X generator of distributions for lifetime data. Journal of Statistical Theory and Applications, 16, 288-305.
- Yousof, H. M., Rasekhi, M., Afify, A. Z., Alizadeh, M., Ghosh, I. and Hamedani G. G. (2017b). The beta Weibull-G family of distributions: theory, characterizations and applications, Pakistan Journal of Statistics, 33, 95-116.
- Yousof, H. M., Alizadeh, M., Jahanshahiand, S. M. A., Ramires, T. G., Ghosh, I. and Hamedani G. G. (2017c). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, Journal of Data Science, 15, 723-740.