STATISTICAL PROPERTIES OF LOMAX-INVERSE EXPONENTIAL DISTRIBUTION AND APPLICATIONS TO REAL LIFE DATA
Abstract
This paper proposes a Lomax-inverse exponential distribution as an improvement on the inverse exponential distribution in the form of Lomax-inverse Exponential using the Lomax generator (Lomax-G family) with two extra parameters to generalize any continuous distribution (CDF). The probability density function (PDF) and cumulative distribution function (CDF) of the Lomax-inverse exponential distribution are defined. Some basic properties of the new distribution are derived and extensively studied. The unknown parameters estimation of the distribution is done by method of maximum likelihood estimation. Three real-life datasets are used to assess the performance of the proposed probability distribution in comparison with some other generalizations of Lomax distribution. It is observed that Lomax-inverse exponential distribution is more robust than the competing distributions, inverse exponential and Lomax distributions. This is an evident that the Lomax generator is a good probability model.
References
Abdullahi, J; Abdullahi, U.K; Ieren, T.G; Kuhe, D.A; Umar, A, A. (2018). On the properties and applications of transmuted odd generalized exponential- exponential distribution. Asian Journal of Probability and Statistics.;1(4):1-14.
Abd-Elfattah, A.M; Alaboud, F.M; and Alharby, A.H. (2007). On sample size estimation for Lomax distribution. Austr. J. Bas. Appl. Sci.1:373-378.
Abouammoh, A.M and A.M. Alshingiti, (2009). Reliability estimation of generalized inverted exponential distribution. J. Stat. Comput. Simul., 79:1301-1315.
Al-Awadhi, S.A; and Ghitany, M.E (2001). Statistical properties of Poisson-Lomax distribution and its application to repeated accidents data. J. Appl. Stat. Sci.10 (4):365-372.
Afify, A.Z. and Aryal, G. (2016). The Kummaraswamy exponentiated Frechet distribution. Journal of Data Science, 6: 1-19.
Balakrishnan, N, and Ahsanullah, M. (1994). Relations for single and product moments of record values from Lomax distribution. Sank. B.56:140-146.
Barreto-Souza, W. M., Cordeiro, G. M. and Simas, A. B. (2011). Some results for beta Frechet distribution. Communications in Statistics- Theory and Methods, 40: 798-811.
Bourguignon, M., Silva, R. B. and Cordeiro, G. M. (2014). The Weibull-G family of Probability Distributions. Journal of Data Science, 12: 53-68.
Chen, G. and Balakrishnan, N. (2018). General Purpose Approximation Googness-of-Fit test. Journal of Quality Technology27:2; 154-161. Doi: 10.1080|00224065
Cordeiro, G. M., Ortega, E. M. M., Popovich,
B. V and Pescim, R. R. (2014). The Lomax Generator of distributions: Properties, Minification process and regression model. Applied Mathematics and Computation,
:465-486.
Efron, B. (1988). Logistic regression, survival analysis and the Kaplan-Meier curve, Journal of the American Statistical Association, 83, pp. 414–425.
El-Bassiouny, A.H; Abdo, N.; and Shahen, H.S (2015). Exponential Lomax distribution. International Journal of Computer Applications;47:4,800 -816
Ghitany M.E; Al-Awadhi, F.A; Alkhalfan, L.A.(2007) Marshall-Olkin extended Lomax distribution and its application to censored Data. Comm. Stat.Theo. Meths. 36:1855-1866.
Hassan, A.S. and Al-Ghamdi, A.S. (2009) Optimum step Stress accelerated life testing for Lomax Distribution. J. Appl. Sci. Res.2009; 5(12):2153-2164.
Ieren, T.G; Abdulkadir, S.S; and Issa, A.A. (2020), Odd Lindley-Rayleigh Distribution: Its Properties and Applications to Simulated and Real life Datasets. Journal of Advances
in Mathematics and Computer Science; 35(1):63 – 88
Ieren T.G; and Chukwu, A.U (2018). Bayesian estimation of a shape parameter of the Weibull-Frechet distribution. Asian J. of
Prob. and Stat.2 (1):1-19. DOI: 10.9734/AJPAS/2018/44184
Ieren, T. G; Koleoso; P. O; Chama, A. F; Eraikhuemen; I. B; Yakubu, N .A. (2019) A Lomax inverse Lindley Distribution:
Model Properties and Application to Real Life Data. Journal of Advances in Mathematics and Computer Science, 34(3 –
:1 – 28
Ieren, T.G. and Kuhe, A. D.(2018). On the Properties and Applications of Lomax-Exponential Distribution. Asian J. Prob. Stat., 1(4):1-13.
Ijaz, M; Asim, S.M and Alamgir, (20919). Lomax exponential Distribution with an Application to Real- life data. PLoS ONE 14(12) e0225827 https://doi.org/10.137/ journal.pone.0225827
Keller, A. Z. and Kamath, A. R. (1982).Reliability analysis of cnc machine tools. Reliability Engineering, 3: 449-473.
Lee, E.T; and Wang, J.W (2003). Statistical methods for survival data analysis. John Wiley and Sons, 3rd Edn.New York. ISBN: 9780471458555. 534.
Lemonte, A.J and Cordeiro, G.M (2013). An Extended Lomax Distribution. Journal of Theoretical and Applied Statistics; 47:4,800 – 816
Maiti, S.S; Pramanik S. (2015) Odds generalized exponential-exponential distribution. J. of Data Sci. 13:733-754
Mundher, A.K; and Ahmed, M.T (2017) New Generalization of the Lomax distribution with increasing and constant Failure rate.Modelling and Simulation in Engineering.ID6043169,6 pages|https://doi.org/10/1155
Oguntunde, P. E. and Adejumo, A. O. (2015). The transmuted inverse exponential distribution. Inter. J. Adv. Stat. Prob. 3(1):1–7
Oguntunde, P. E., Balogun, O. S, Okagbue, H. I, and Bishop, S. A. (2015). The Weibull- Exponential Distribution: Its Properties and Applications. Journal of Applied Science.15 (11): 1305-1311.
Omale, A; Yahaya, A, and Asiribo, O.E. (2019). On properties and applications of Lomax-GompertzDistribution. Asian J. Prob. Stat.3 (2):1-17.
Owoloko, E.A; Oguntunde, P.E; Adejumo, A.O. (2015).Performance rating of the transmuted exponential distribution: an analytical approach. Spring. 2015; 4:818-829.
Rady E.A, Hassanein, W.A; Elhaddad, T.A,(2016). The power Lomax distribution with an application to bladder cancer data. Springer Plus.5 (1)1838. DOI: 10.1186/s40064-016-3464-y.
Sandhya, E.and Prasanth, C.B ((2014), Marshall-Olkin discrete uniform Distribution. Journal of Probability 1- 10. doi.1011551/2014/979312
Shanker, R., Hagos, F., and Sujath, S., (2015). On modeling of Lifetimes data using exponential and Lindley distributions, Biometrics& Biostatistics International Journal, 2 (5), pp. 1–9.
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: 358-369.
Venegas, O; Iriarte, Y.A; and Astorga, J.M. (2019) Gomez HW, Lomax-Rayleigh distribution with an application. Appl. Math. Inf. Sci., 13(5):741-748
Copyright (c) 2020 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
