Theoretical Analysis of the Weibull Alpha Power Inverted Exponential Distribution: Properties and Applications

Year 2020, Volume: 33 Issue: 1, 265 - 277, 01.03.2020

Eferhonore Efe-eyefıa Joseph Thomas Samuel Chiabom Zelıbe

https://doi.org/10.35378/gujs.537832

Cited By: 16

Abstract

This article proposed a Weibull-Alpha Power Inverted Exponential (WAPIE) distribution for lifetime processes. Statistical properties of this distribution such as survival, hazard, reversed hazard, cumulative, odd functions, kurtosis, quantiles, skewness, order statistics and the entropies were derived. Parameters of this family of distribution were also obtained by maximum likelihood method. The behaviour of the estimators was studied through simulation. The behavior of the new developed distribution was further examined through real life data. The WAPIE distribution competes favourably well with other distributions. 

Keywords

Alpha Power, Inverted Exponential, Life Time Distribution, Maximum Likelihood, Weibull

References

• Anake, T. A., Oguntunde, P. E., Odetunmibi, O. A. “On a Fractional Beta-Exponential Distribution”. International Journal of Mathematics and Computations, 26(1), 26-34, (2015).
• Weibull, W. “A statistical distribution function of wide applicability”. Journal of Applied Mechanics, Transactions, 18, 293-297, (1951).
• Korkmaz, M., Alizadeh M., Yousof, H. M., Butt, N. S. “The Generalized Odd Weibull Generated Family of Distributions: Statistical Properties and Applications”, Pakistan Journal of Statistics and Operation Research, 3, 541- 556, (2018).
• Gupta, R. D., Kundu, D. “Generalized exponential distribution”. Australian and New Zealand Journal of Statistics, 41 (2), 173-188, (1999).
• Gupta, R. C, Gupta, P. I. & Gupta, R. D. “Modeling failure time data by Lehmann alternatives”, Communications in Statistics-Theory and Methods, 27, 887-904, (1998).
• Oguntunde, P.E., Babatunde, O.S., Ogunmola, A.O., “Theoretical Analysis of the Kumaraswamy-inverse Exponential Distribution”, International Journal of Statistics and Applications, 4(2), 113-116, (2014a).
• Oguntunde, P.E., Adejumo, A., Balogun, O.S. “Statistical Properties of the Exponentiated Generalized Inverted Exponential Distribution”, Applied Mathematics, 4(2), 47-55, (2014b).
• Oguntunde, P., Adejumo, O. “The Transmuted Inverse Exponential Distribution”. International Journal of Advanced Statistics and Probability, 3(1), 1-7 (2014c).
• Aryal, G. R., Yousof, H. M. “The exponentiated generalized-G Poisson family of distributions”. Economic Quality Control, 32(1), 1-17, (2017).
• Nofal, Z. M., Affy, A. Z., Yousof, H. M., Cordeiro, G. M. “The generalized transmuted-G family of distributions”, Communications in Statistics Theory and Methods, 46, 4119-4136, (2017).
• Yousof, H. M., Altun, E., Ramires, T. G., Alizadeh, M., Rasekhi, M. “A new family of distributions with properties, regression models and applications”, Journal of Statistics and Management Systems, 21(1), 163-188, (2018).
• Cordeiro, G. M., Ortega, E. M. & da Cunha, D. C. C. “The exponentiated generalized class of distributions”, Journal of Data Science, 11, 1-27, (2013).
• Cordeiro, G.M., Ortega, E.M.M., Nadarajah, S. “The Kumaraswamy Weibull distribution with application to failure data”, Journal of the Franklin Institute, 347, 1317-1336, (2010).
• Cordeiro, G.M., Hashimoto, E.M., Ortega, E.M.M. “The McDonald Weibull model. Statistics”, Journal of Theoretical and Applied Statistics, 48, 256-278, (2014).
• Yousof, H. M., Affy, A. Z., Hamedani, G. G., Aryal, G., “The Burr X generator of distributions for lifetime data”, Journal of Statistical Theory and Applications, 16, 288-305, (2017a)
• Yousof, H. M., Rasekhi, M., A_fy, A. Z., Alizadeh, M., Ghosh, I., Hamedani G. G. “The beta Weibull-G family of distributions: theory, characterizations and applications”, Pakistan Journal of Statistics, 33, 95-116, (2017b).
• Yousof, H. M., Alizadeh, M., Jahanshahiand, S. M. A., Ramires, T. G., Ghosh, I., Hamedani G. G. “The transmuted Topp-Leone G family of distributions: theory, characterizations and applications”, Journal of Data Science, 15, 723-740, (2017c).
• Oguntunde, P.E., “Generalisation of the Inverse Exponential Distribution: Statistical Properties and Applications”.Phd. Thesis, Covenant University College of Science and Technology, Ota, Ogun State, 128—142, (2017a).
• Oguntunde, P., Khaleel, M. A., Ahmed, M. T., Adejumo, A. O. ,Odetunmibi O. A. “A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate”,Hindawi Modelling and Simulation in Engineering, 1—7, (2017b).
• Oguntunde, P. E., Odetunmibi, O. A., Adejumo, A. O. “On Sum of Exponentialially Distributed Random Variables”. A Convolution Approach. European Journal of Statistics and Probability, 1(2). 1-8, (2013).
• Keller, A. Z., Kamath, A. R. R., &Perera, U. D., “ Reliability analysis of CNC machine tools”, Reliability Engineering, 3(6): 449-473, (1982).
• Lin, C.T., Duran, B.S., Lewis, T.O., “Inverted gamma as a life distribution”, Microelectronics Reliability, 29(4), 619-626, (1989).
• Abouammoh, A.M., Alshingiti, A.M. “Reliability estimation of generalized inverted exponential distribution”, Journal of Statistical Computation and Simulation, 79(11), 1301-1315, (2009).
• Dey, S., Alzaatreh, A., Zhang, C., Kumar, D. “A new extension of generalized exponential distribution with application to ozone data”. Ozone: Science and Engineering, 39(4), 273-285, (2017).
• Mahdavi, A., Kundu, D. “A new method for generating distributions with an application to exponential distribution”, Communications in Statistics - Theory and Methods, 46(13), 6543-6557, (2017).
• Nadarajah, S., Okorie I. E. “On the moments of the alpha power transformed generalized exponential distribution”, The Ozone: Science and Engineering, 1--6. (2017).
• Barreto-Souza, W., Simas, A. B. “Theexp-G family of probability distributions”,Brazilian Journal of Probability and Statistics 27:84-109, (2013).
• Nadarajah, S., Nassiri, V., Mohammadpour, A. “Truncated-exponential skewsymmetric distributions”, Statistics 48:872-895, (2014).
• Nassar, M., Alzaatreh, A., Mead, M., Abo-Kasem, O. “Alpha power Weibull distribution: properties and applications”, Communications in Statistics -Theory andMethods 46:10236-10252, (2017).
• Bourguignon M., Silva R. B., Cordeiro G. M. “The Weibull-G Family of Probability Distributions”, Journal of Data Science, 12, 53-68, (2014).
• Unal, C., Cakmakyapan, S., Ozel, G. “Alpha Power Inverted Exponential Distribution: Properties and Application”, Gazi University Journal of Science, 31(3), 954-965, (2018).
• Smith, R. L., Naylor, J. C. “A Comparison of Maximum Likelihood and Bayesian Estimators for the three-parameter Weibull Distribution”, Applied Statistics, 36, 258–369, (1987).
• Haq, M. A., Butt, N. S., Usman, R. M., Fattah, A. A. “Transmuted Power Function Distribution”. Gazi University Journal of Science 29(1), 177–185, (2016).
• Merovci, F., Khaleel, M. A., Ibrahim, N. A., Shitan, M. “The beta type X distribution: properties with application”, Springer-Plus, (5), 697, (2016).
• Rastogi, M. K., Oguntunde, P. E. “Classical and Bayes estimation of reliability characteristics of the Kumaraswamy-Inverse Exponential distribution”, International Journal of System Assurance Engineering and Management. (2018).
• Obubu, M., Oyamakin, S. O., Eghwerido J. T. “The Gompertz Length Biased Exponential Distribution and its application to Uncensored Data”, Current Trends on Biostatistics & Biometrics, 1, 52-57, (2019).
• Nichols, M. D., Padgett, W. J, “A Bootstrap control chart for Weibull percentiles”, Quality and Reliability Engineering International, 22, 141-151, (2016).