On the inferences and applications of transmuted exponential Lomax distribution

  • Abstract
  • Keywords
  • References
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  • Abstract

    This article proposed a new distribution referred to as the transmuted Exponential Lomax distribution as an extension of the popular Lomax distribution in the form of Exponential Lomax by using the Quadratic rank transmutation map proposed and studied in earlier research. Using the transmutation map, we defined the probability density function (PDF) and cumulative distribution function (CDF) of the transmuted Exponential Lomax distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Lomax distribution using three real-life data sets. The results obtained indicated that TELD performs better than the other distributions comprising power Lomax, Exponential-Lomax, and the Lomax distributions.

  • Keywords

    : Lomax Distribution; Quadratic Rank Transmutation Map; Moments; Properties; Maximum Likelihood Estimation; Order Statistics; Transmut-ed Exponential Lomax Distribution; Parameters; Analysis.

  • References

      [1] Abdul-Moniem, I. B. (2012). Recurrence relations for moments of lower generalized order statistics from exponentiated Lomax distribution and its characterization. International Journal Mathematics and Architecture, 3:2144–2150.

      [2] Al-Zahrani, B. (2015). An extended Poisson-Lomax distribution. Advanced Mathematical Science Journal, 4(2): 79–89.

      [3] Al-Zahrania, B. and Sagorb, H. (2014) The Poisson-Lomax distribution. Rev Colomb de Estad 37(1): 223–243. https://doi.org/10.15446/rce.v37n1.44369.

      [4] Ashour, S. and Eltehiwy, M. (2013). Transmuted exponentiated Lomax distribution. Australian Journal of Basic and Applied Sciences, 7(7): 658–667

      [5] Atkinson, A. and Harrison, A. (1978). Distribution of personal wealth in Britain. Cambridge University Press, Cambridge.

      [6] Bryson, M. (1974). Heavy-tailed distributions: properties and tests. Technometrics, 16:61–68 https://doi.org/10.1080/00401706.1974.10489150.

      [7] Corbellini, A., Crosato, L., Ganugi, P. and Mazzoli, M. (2007). Fitting Pareto II distributions on firm size: Statistical methodology andeconomic puzzles. Paper presented at the international conference on applied stochastic models and data analysis, Chania, Crete.

      [8] Cordeiro, G., Ortega, E. and Popović, B. (2013). The gamma-Lomax distribution. Journal Statistical Computation and Simulation, 85(2): 305–319. https://doi.org/10.1080/00949655.2013.822869.

      [9] El-Bassiouny A, Abdo N., Shahen H. (2015) Exponential Lomax distribution. International Journal of Computer Applications, 121(13): 24-29. https://doi.org/10.5120/21602-4713.

      [10] Fuller, E. J., Frieman, S., Quinn, J., Quinn, G. and Carter, W. (1994). Fracture mechanics approach to the design of glass aircraft windows: A case study. SPIE Proc 2286: 419-430.

      [11] Ghitany, M., Al-Mutairi, D., Balakrishnan, N. and Al-Enezi, I. (2013). Power Lindley distribution and associated inference. Computational Statistics and Data Analysis 64: 20-33. https://doi.org/10.1016/j.csda.2013.02.026.

      [12] Ghitany, M. E., AL-Awadhi, F. A. and Alkhalfan, L. A. (2007). Marshall-Olkin extended Lomax distribution and its applications to censored data. Communication in Statistics-Theory and Methods, 36: 1855–1866. https://doi.org/10.1080/03610920601126571.

      [13] Gross, A. J. and Clark, V. A. (1975). Survival distributions reliability applications in the Biometrical Sciences. John Wiley, New York, USA.

      [14] Gupta, R., Ghitany, M. and Al-Mutairi, D. (2010). Estimation of reliability from Marshall–Olkin extended Lomax distributions. Journal of Statistical Computation and Simulation, 80: 937–947 https://doi.org/10.1080/00949650902845672.

      [15] Harris, C. (1968). The Pareto distribution as a queue service discipline. Operations Research, 16: 307–313. https://doi.org/10.1287/opre.16.2.307.

      [16] Hassan, A. and Al-Ghamdi, A. (2009). Optimum step stress accelerated life testing for Lomax distribution. Journal of Applied Science Research, 5: 2153–2164.

      [17] Holland, O. Golaup, A. and Aghvami, A. (2006). Traffic characteristics of aggregated module downloads for mobile terminal reconfiguration. In: IEE proceedings—communications, 135: 683–690. https://doi.org/10.1049/ip-com:20045155.

      [18] Ieren, T. G. and Yahaya, A. (2017). The Weimal Distribution: its properties and applications. Journal of the Nigeria Association of Mathematical Physics, 39: 135-148.

      [19] Kenney, J. F. and Keeping, E. S. (1962). Mathematics of Statistics, 3 edn, Chapman & Hall Ltd, New Jersey.

      [20] Lemonte, A. and Cordeiro, G. (2013). An extended Lomax distribution. Statistics, 47: 800–816 https://doi.org/10.1080/02331888.2011.568119.

      [21] Lomax, K. S. (1954). Business failures: Another example of the analysis of failure data, Journal of the American Statistical Association, 49: 847–852. https://doi.org/10.1080/01621459.1954.10501239.

      [22] Moors, J. J. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D, 37: 25–32. https://doi.org/10.2307/2348376.

      [23] Rady, E. A., Hassanein, W. A. and Elhaddad, T. A. (2016). The power Lomax distribution with an application to bladder cancer data. SpringerPlus (2016) 5:1838 https://doi.org/10.1186/s40064-016-3464-y.

      [24] Shanker, R., Fesshaye, H. and Sharma, S. (2016). On two-Parameter Lindley distribution and its applications to model life time data. Biom. Biostat. Int. J., 3(1): 00056. https://doi.org/10.15406/bbij.2016.03.00056.

      [25] Shaw, W. T. and Buckley, I. R. (2007). The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research report.

      [26] Tahir, M., Cordeiroz, G., Mansoorx M. and Zubair, M. (2015). The Weibull-Lomax distribution: properties and applications. Hacet J Math Stat 44(2):461–480.

      [27] Zografos, K. and Balakrishnan, N. (2009). On families of beta- and generalized gamma generated distributions and associated inference. Statistical Methodology, 6:344–362. https://doi.org/10.1016/j.stamet.2008.12.003.




Article ID: 8129
DOI: 10.14419/ijasp.v6i1.8129

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