IJARP SJIF(2018): 4.908

International Journal of Advanced Research and Publications!

Exponential Pareto Negative Binomial Distribution With Its Properties And Application

Volume 4 - Issue 4, April 2020 Edition
[Download Full Paper]

Akomolafe, A. A., Oladejo,O. M., Bello, A. H. and Ajiboye, A. S.
Moment Generating Function, Survival Rate, Harzard rate, Exponential Pareto Negative Binomial Distribution, Maximum Likelihood Method.
In this research, we consider certain results characterizing the generalization of Exponential Pareto and Negative Binomial Distribution through their distribution functions and asymptotic properties. The resulting Exponential Pareto Negative Binomial Distribution [EPNBD] was defined and some of its properties like moment generating function, survival rate function, hazard rate function and cumulative distribution function were investigated. The estimation of the model parameters was performed using maximum likelihood estimation method. The distribution was found to generalize some known distributions thereby providing a great flexibility in modeling symmetric, heavy tailed, skewed and bimodal distributions, the use of the new lifetime distribution was illustrated using failure time life data.
[1]. Akinsete,A.,Famoye,F., and Lee,C.,(2008). The beta- pareto distribution, Statistics 42(6), 547-563.

[2]. Akomolafe A.A and Maradesa A., (2017). Beta-halfnormal Distribution and Its Properties,

[3]. International journal of Advance Research and Publication vol (1) issued 4 (17-22).

[4]. Akomolafe, A.A and A. Maradesa. 2017. “Beta-halfnormal Distribution and Its Properties.” International journal of Advance Research and Publication 1(4):17-22.

[5]. Akomolafe, A. A. and Yussuf, T. O. (2018). Dirichilet- Multinomial Model: its mixture and Application using Bayesian Approach. Rep Opinion 10(2) 1-15. http://www.sciencepub.net/report doi: 10:7517/marsroj100518.03.

[6]. Akomolafe, A. A., Maradesa, A. and Yusuf, T. O. (2018): Beta-Binomial Mixture Models: Its Consistence and Efficient Performance over Binomial models. Indo-Iranian Quarterly International Journal. 2(2) 11-23. http://www.iijsr.com

[7]. Akomolafe, A. A., (2018): Investigating Customer Behaviour Heterogeneity using Exponential -Gamma Timing Model. Rep and Opinion 10(5) 25-31. http://www.sciencepub.net/report. doi: 10:7517/marsroj100518.03.

[8]. Albert, L., and Suleman, N., (2015). Transmuted Exponential Pareto distribution, Far East

[9]. Journal of Theoretical statistics, 50(1):31-49. http://dx.doi.org/10.17654/FJTSJan2015_031_049

[10]. Alzaatreh, A., F. Famoye and C. Lee, (2013). Weibull-Pareto distribution and its applications.

[11]. Communication in Statistics,Theory-Methods, 42: page1673-1691.

[12]. Ashour S.K and Eltehiwy M.A., (2013).Transmuted Lomax distribution, America Journal of Applied Mathematics and Statistics vol1, 6:121-127.

[13]. Badmus, N.I., Ikegwu,M.and Emmanuel,(2013).The Beta-Weighted Weibull Distribution: Some properties and application to Bladder Cancer Data, Applied and Computational Mathematics,2:5.

[14]. Barreto-Souza W, De Morais A, Cordeiro G. (2011).The Weibull-Geometric distribution. J. Stat Comput Simul.81(5):page 645–657

[15]. Bourguignon, M., R.B. Silva and G.M. Cordeiro, (2014). Theweibull-G family of probabilitydistributions. J. Data Sci.,12: page 53-68.

[16]. Cooray, K. and Ananda, M. (2005). Modeling actuarial data with a compositelognormal-Paretomodel. Scandinavian Actuarial Journal 5, page 321-334.

[17]. Cordeiro, G.M. and M. de Castro, 2011. A new family ofgeneralized distributions. J. Stat. Comput. Simul.,81: page 883-898.

[18]. Demétrio And Edwin M. M. Ortega.(2011). Advances and Applications in StatisticsVolume 22, Number 1, Pages 25-55.

[19]. Doostparast, M., and Balakrishnan, N. (2013).Pareto Analysis Based on Records.Statistics,47: page 1075-1089.

[20]. Essam A. Amin(2017). On Record Values of Exponential Pareto Distribution, Department of Mathematical Statistics, Institute of Statistical Studies and Research. Applied Mathematical Sciences.Vol.11, 2017, no. 32,page 1547–1559.HIKARI Ltd,www.m-hikarihttps://doi.org/10.12988/ams.2017.74154.

[21]. Famoye F, Lee C, Olumolade O. (2005). The beta-weibull distribution. J Stat Theory Appl.;4: page121–136.

[22]. Francisco Louzada, Vicente G. Cancho and Bao Yiqi (2015).The Log-Weibull-Negative-Binomial Regression Model Under Latent Failure Causes And Presence Of Randomized Activation Schemes.

[23]. A. Gupta, R.D. and D. Kundu, (2001). Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical J., 43: page 117-130.

[24]. Keller, A.Z., Kamath A.R.R. and Perera, U.D. (1982).Reliability analysis of CNC machine tools. Reliabil. Eng.,3: page 449-473.

[25]. Lai C, Xie M and Murthy D. (2003). A modified Weibull distribution. IEEE Trans Reliab.;52: page 33–37.

[26]. Merovci F. and Puka L.,(2014). Transmuted Pareto Distribution, Probability statistics Forum Vol 7, (1-11). Mahmoud M.R. and Mandouh R.M., (2013). Transmuted frechet, Journal of Applied Science Research vol9 no 10 pp(555-561) Marcelo B., Indranil G., and Cordeiro G.M., (2016), General results for the transmuted Family of Distributions and New Models, Journal of Probability and Statistics. Mudholkar G, Srivastava D. (1993). Exponentiated Weibull family for analyzing bathtub failure-ratedata. IEEE TransReliab.;42(2):page 299–302.

[27]. Mohammad D., and Muhammad A., (2014), on the Mixture of BurrXII and Weibull Distribution, Journal of Statistics Application and Probability, J.Sta.Appl.Pro. 3, No 2, 251-267. Nadarajah, S. and S, Kotz(2006). The beta-exponentialdistribution. Reliab., 91:page 689-697.

[28]. NareeratNanuwong [a], WinaiBodhisuwan [a] and ChookaitPudprommarat [b]. (2015).; 13(2): page 191-207 http://statassoc.or.th. Thailand.

[29]. Nasiru, S. and A, Luguterah.(2015). The new weibull-paretodistribution. Pak. J. Stat. Operat. Res., 11: page 103-114.

[30]. Okorie E., Akpanta A.C., and Ohakwe J., (2016). The exponential Gumbel Type 2 Distribution: Properties and Application, international Journal of Mathematics and Mathematical ScienceVolume (2016), Article ID 5898356, 10 pageshttp://dx.doi.org/10.1155/2016/5898356