Araştırma Makalesi
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Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications

Yıl 2019, Cilt: 12 Sayı: 1, 35 - 48, 31.07.2019

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

Öz

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.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Joseph Thomas Bu kişi benim 0000-0001-8986-753X

Samuel Chiabom Zelibe Bu kişi benim

Eferhonore Eyefia Bu kişi benim

Yayımlanma Tarihi 31 Temmuz 2019
Kabul Tarihi 12 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 1

Kaynak Göster

APA Thomas, J., Zelibe, S. C., & Eyefia, E. (2019). Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications. Istatistik Journal of The Turkish Statistical Association, 12(1), 35-48.
AMA Thomas J, Zelibe SC, Eyefia E. Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications. IJTSA. Temmuz 2019;12(1):35-48.
Chicago Thomas, Joseph, Samuel Chiabom Zelibe, ve Eferhonore Eyefia. “Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications”. Istatistik Journal of The Turkish Statistical Association 12, sy. 1 (Temmuz 2019): 35-48.
EndNote Thomas J, Zelibe SC, Eyefia E (01 Temmuz 2019) Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications. Istatistik Journal of The Turkish Statistical Association 12 1 35–48.
IEEE J. Thomas, S. C. Zelibe, ve E. Eyefia, “Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications”, IJTSA, c. 12, sy. 1, ss. 35–48, 2019.
ISNAD Thomas, Joseph vd. “Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications”. Istatistik Journal of The Turkish Statistical Association 12/1 (Temmuz 2019), 35-48.
JAMA Thomas J, Zelibe SC, Eyefia E. Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications. IJTSA. 2019;12:35–48.
MLA Thomas, Joseph vd. “Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications”. Istatistik Journal of The Turkish Statistical Association, c. 12, sy. 1, 2019, ss. 35-48.
Vancouver Thomas J, Zelibe SC, Eyefia E. Kumaraswamy Alpha Power Inverted Exponential Distribution: Properties and Applications. IJTSA. 2019;12(1):35-48.