Journal of Advances in Applied Mathematics

Download PDF (298.1 KB) PP. 75 - 81 Pub. Date: April 1, 2019

DOI: 10.22606/jaam.2019.42005

• Obubu Maxwell^*
  Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria
• Samuel Oluwafemi Oyamakin
  Department of Statistics, University of Ibadan, Ibadan, Nigeria
• Angela Chukwu Unna
  Department of Statistics, University of Ibadan, Ibadan, Nigeria
• Adeleke Akinrinade Kayode
  Department of Statistics, University of Ilorin, Ilorin, Nigeria
• Yusuf Olufemi Olusola
  Department of Statistics, University of Ilorin, Ilorin, Nigeria

This article proposes a new continuous lifetime model called the Gompertz Alpha Power Inverted Exponential (G-APIE) distribution, and compares its modelling strength between the Extended Exponential distribution, Exponential Weibull, and Exponentiated Lomax distribution. The proposed distribution was applied to three lifetime data and the best model determined based on the lowest criterion values.

Alpha power, inverted exponential, order statistics, Gompertz generalized family of distribution, hazard functions.

[1] Abouammoh, A. M. & A. M. Alshingiti (2009). Reliability estimation of generalized inverted exponential distribution. Journal of Statistical Computation and Simulation 79 (11), 1301-1315.

[2] Afify, A. Z., E. Altun, M. Yousof, H. M.and Alizadeh, G. Ozel, & G. G. Hamedani (2017). The odd exponentiated half-logistic-g family: Properties, characterizations and applications. Chilean Journal of Statistics 8 (2), 65-91.

[3] Alizadeh, M., Cordeiro, G. M. Pinho, L. G. B. & I. Ghosh (2017). The Gompertz-g family of distributions. Journal of Statistical Theory and Practice 11 (1), 179-207.

[4] Anake, T. A., Oguntunde, F. E. & Odetunmibi, A. O. (2015). On a fractional beta-exponential distribution. International Journal of Mathematics and Computations 26 (1), 26-34.

[5] Aryal, G. R. & Yousof H. M.(2017). The exponentiated generalized-g poisson family of distributions. Economic Quality Control 32 (1), 1-17.

[6] Bourguinon, M., B., Silva, R. & Cordeiro, G. M. (2014). The weibull-g family of probability distributions. Journal of Data Science 12, 53-68.

[7] Cordeiro, G. M., Ortega, E. M. & da Cunha D. C. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science 11, 1-27.

[8] Haq, M. A., Butt, N. S., Usman, R. M. & Fattah, A. A. (2016). Transmuted power function distribution. Gazi University Journal of Science 29 (1), 177-185.

[9] Keller, A. Z., Kamath, A. R. R. & Perera, U. D. (1982). Reliability analysis of cnc machine tools. Reliability Engineering 3 (6), 449-473.

[10] Lee, C., Famoye, F. & Alzaatreh A. Y. (2013). Methods for generating families of univariate continuous distributions in the recent decades. Wiley Interdisciplinary Reviews: Computational Statistics 5 (3), 219-238.

[11] Lin, C. T., Duran, B. S. & Lewis, T. O. (1989). Inverted gamma as a life distribution. Microelectronics Reliability 29 (4), 619-626.

[12] Mahdavi, A. & 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.

[13] Merovci, F., Khaleel, M. A., Ibrahim, N. A. & Shitan, M. (2016). The beta type-x distribution: properties with application. Springer-Plus 5, 697.

[14] Nadarajah, S. & Okorie, I. E. (2017). On the moments of the alpha power transformed generalized exponential distribution. Ozone: Science and Engineering, 1-6.

[15] Nichols, M. D. & Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International 22, 141-151.

[16] Oguntunde, P. E, & Adejumo, O. A, (2014). The transmuted inverse exponential distribution. International Journal of Advanced Statistics and Probability 3 (1), 1-7.

[17] Maxwell O, Friday AI, Chukwudike NC, et al. (2019). A theoretical analysis of the odd generalized exponentiated inverse Lomax distribution. Biom Biostat Int J. 2019; 8(1): 17-22. DOI: 10.15406/bbij.2019.08.00264.

[18] Pinho, L. G. B., Cordeiro, G. M. & Nobre, J. S. (2015). The harris extended exponential distribution. Communications in Statistics -Theory and Methods 44 (16), 3486-3502.

[19] Rastogi, M. K. & Oguntunde, P. E. (2018). Classical and bayes estimation of reliability characteristics of the kumaraswamy-inverse exponential distribution. International Journal of System Assurance Engineering and Management.

[20] Smith, R. L. & J. C. Naylor (1987). A comparison of maximum likelihood and Bayesian estimators for the threeparameter weibull distribution. Applied Statistics 36, 258-369.

[21] Unal, C., S. Cakmakyapan, & Ozel, G. (2018). Alpha power inverted exponential distribution: Properties and application. Gazi University Journal of Science 31 (3), 954-965.

[22] Jafari, A., Tahmasebi, S. and Alizadeh, M. (2014). The beta-gompertz distribution, Revista Colombiana de Estadistica, 37(1): 139-156.

[23] Shittu, O. I. and Adepoju, K. A. (2013). On the beta-nakagami distribution, Progress in Applied Mathematics, 5(1): 49-58.

[24] Huang, S. and Oluyede, B. (2014). Exponentiated kumaraswamy-dagum distribution with applications to income life data, Journal of Statistical Distributions and Applications, 1(8): 1-20. DOI: 10.1186/2195-5832-1-8.

[25] Owoloko, E. A., Oguntunde, P. E. and Adejumo, A. O. (2015). Performance rating of the transmuted exponential distribution: an analytical approach, SpringerPlus, 4(1): 1-15.

[26] Obubu Maxwell, Samuel Oluwafemi Oyamakin, Eghwerido Joseph Th. The Gompertz Length Biased Exponential Distribution and its application to Uncensored Data. Curr Tre Biosta & Biometr 1(3) -2018. CTBB.MS.ID.000111.

[27] Maxwell O, Chukwudike NC, Bright OC. Modeling lifetime data with the odd generalized exponentiated inverse Lomax distribution. Biom Biostat Int J. 2019; 8(2): 39-42. DOI: 10.15406/bbij.2019.08.00268.