Gamze ÖZEL, Ceren ÜNAL, Selen ÇAKMAKYAPAN

Alpha Power Inverted Exponential Distribution: Properties and Application

In this study, we introduce a new distribution based on the inverted exponential distributioncalled as “Alpha Power Inverted Exponential” distribution. Some of the statistical properties areprovided such as hazard rate function, quantile function, skewness, kurtosis, and order statistics.Model parameters are obtained by the maximum likelihood. We prove empirically importanceand flexibility of the new distribution in modeling with real data applications.

PDF

___

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).
Oguntunde, P.E., Adejumo, A., Owoloko, E.A., “On the exponentiated generalized inverse exponential distribution”, World Congress on Engineering, London, 80-83, (2017).
Singh, S.K., Singh, U., Kumar, D., “Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors”, Journal of Statistical Computation and Simulation, 83(12): 2258-2269, (2013).
Dey, S., “Inverted exponential distribution as a life distribution model from a bayesian viewpoint”, Data Science Journal, 6: 107-113, (2007).
Abouammoh, A.M., Alshingiti, A.M., “Reliability estimation of generalized inverted exponential distribution”, Journal of Statistical Computation and Simulation, 79(11): 1301-1315, (2009).
Oguntunde, P.E., Adejumo, A., Balogun, O.S., “Statistical properties of the exponentiated generalized inverted exponential distribution”, Applied Mathematics, 4(2): 47-55, (2014).
Singh, S.K., Singh, U., Kumar, M., “Estimation of parameters of generalized inverted exponential distribution for progressive Type-II censored sample with binomial removals”, Journal of Probability and Statistics, Doi:10.1155/2013/183652, (2013).
Oguntunde, P.E., Babatunde, O.S., Ogunmola, A.O., “Theoretical analysis of the kumaraswamyinverse exponential distribution”, International Journal of Statistics and Applications, 4(2): 113-116, (2014).
Oguntunde, P., Adejumo, O., “The transmuted inverse exponential distribution”, International Journal of Advanced Statistics and Probability, 3(1): 1-7, (2014).
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 (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).
Lee, C., Famoye, F., Alzaatreh, A.Y., “Methods for generating families of univariate continuous distributions in the recent decades”, Wiley Interdisciplinary Reviews: Computational Statistics, 5(3): 219-238, (2013).
Dey, S., Alzaatreh, A., Zhang, C., Kumar, D., “A new extension of generalized exponential distribution with application to ozone data”, Ozone: Science & Engineering, 39(4): 273-285, (2017).
Dey, S., Sharma, V.K., Mesfioui, M., “A new extension of weibull distribution with application to lifetime data”, Annals of Data Science, 4(1): 31-61, (2017).
Isik, H., Turfan, D., Ozel, G., “The double truncated dagum distribution with applications”, International Journal of Mathematics and Statistics, 18(2): 61-78, (2017).
Kenney, J.F., Mathematics of Statistics Part 1., Chapman & Hall, London, (1939).
Moors, J.J.A., “A quantile alternative for kurtosis”, The Statistician, 37(1): 25-32. (1988).
Shanker, R., Shukla, K.K., Fesshaye, H., “On weighted lindley distribution and its applications to model lifetime data”, Jacobs Journal of Biostatistics, 1(1): 002, (2016).
Shanker, R., Shukla, K.K., Mishra, A., “A three-parameter weighted lindley distribution and its applications to model survival time”, Statistics, 18(2): 291-310, (2017).
Singh, S.K., Singh, U., Yadav, A., Viswkarma, P.K., “On the estimation of stress strength reliability parameter of inverted exponential distribution”, International Journal of Scientific World, 3(1): 98- 112, (2015).
Sharma, V.K., Singh, S.K., Singh, U., Agiwal, V., “The inverse lindley distribution: A stress-strength reliability model”, arXiv: 1405.6268, (2014).
Efron, B., “Logistic regression, survival analysis and the kaplan-meier curve”, Journal of the American Statistical Association, 83(402): 414-425, (1988).