Beta transmuted Lomax distribution with applications

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics , Statistics & Probability

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ISSN: 1234-7655
eISSN: 2450-0291

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VOLUME 21 , ISSUE 2 (June 2020) > List of articles

Beta transmuted Lomax distribution with applications

Ahmed Hurairah / Abdelhakim Alabid

Keywords : Lomax distribution, beta Lomax distribution, transmuted distribution, maximum likelihood estimation

Citation Information : Statistics in Transition New Series. Volume 21, Issue 2, Pages 13-34, DOI: https://doi.org/10.21307/stattrans-2020-012

License : (CC BY-NC-ND 4.0)

Received Date : 18-May-2018 / Accepted: 13-March-2020 / Published Online: 01-June-2020

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ABSTRACT

In this paper we propose and test a composite generalizer of the Lomax distribution .The genesis of the beta distribution and transmuted map is used to develop the so-called beta transmuted Lomax (BTL) distribution. The properties of the distribution are discussed and explicit expressions are derived for the moments, mean deviations, quantiles, distribution of order statistics and reliability. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators is assessed by simulation. Finally, the authors demonstrate the usefulness of the new distribution in analysing positive data.

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ABDULLAHII, U. A., IEREN, T. G., (2018). On the inferences and applications of transmuted  exponential Lomax distribution, International Journal of Advanced Statistics and Probability, Vol. 6(1), pp. 30–36.

ABDUL-MONIEM, I. B., ABDEL-HAMEED, H. F., (2012). On exponentiated Lomax distribution, International Journal of Mathematical Archive, Vol.3, pp. 144–2150.

ABD-ELFATTAH, A. M., ALABOUD, F. M., ALHARBEY, H. A., (2007). On Sample Size Estimation for Lomax Distribution, Australian Journal of Basic and Applied Sciences, Vol. 1(4), pp. 373–378.

ABD-ELFATTAH, A. M., ALHARBEY, H. A., (2010). Estimation of Lomax Parameters based on Generalized Probability Weighted Moment, JKAU: Science, Vol. 24(2), pp. 171–184.

AHSANULLAH, M., (1991). Record values of the Lomax Distribution, Statistica Neerlandica, Vol. 45, pp. 21–29.

AL-ZAHRANI, B., (2012). Goodness-of-fit for the Topp-Leone distribution with unknown parameters, Applied Mathematical Sciences, Vol. 6(128), pp. 6355–6363.

ASHOUR, S. K., ELTEHIWY, M. A., (2013). Transmuted Lomax Distribution, American Journal of Applied Mathematics and Statistics, Vol. 1(6), pp. 121–27.

AL-AWADHI, S. A., GHITANY, M. E., (2001). Statistical properties of Poisso-Lomax Distribution and its application to repeated accidents data, Journal of Applied Statistical Science, Vol. 10(4), pp. 365–372.

BALKEMA, A. A., DE HAAN, L., (1974). Residual life time at great age, Annuals of Probability, Vol. 2, pp. 792–804.

BALAKRISHNAN, N., AHSANULLAH, M., (1994). Relations for single and product moments of record values from Lomax distribution, Sankhya B, Vol. 56, pp. 140– 146.

BINDU, P., SANGITA, K., (2015). Double Lomax Distribution and its Applications, Statistics, anno LXXV(3), pp. 331–342.

CHILDS, A., BALAKRISHNAN, N., MOSHREF, M., (2001). Order statistics from nonidentical right truncated Lomax random variables with applications, Statistics: Politics, arts, philosophy, Vol. 42(2), pp.187–206.

CORDEIRO, G. M., NADARAJAH, S., (2011). Closed form expressions of moments of a class of a beta generalized distributions, Brazilian Journal of Probability and Statistics,  Vol. 25, pp. 14–33.

CORDEIRO, G. M., ORTEGA, E. M. M., POPOVIC, B. V., (2013). The gamma-Lomax distribution, Journal of Statistical computation and Simulation iFirst, doi:10.1080/00949655.822869.

EUGENE, N., LEE, C., FAMOYE, F., (2002). Beta-normal Distribution and its Applications, Communications in Statistics – Theory and Methods, Vol. 31, pp. 497– 512.

GHITANY, M. E., AL-AWADHI, F. A., ALKHALFAN, L. A., (2007). Marshall-Olkin extended Lomax Distribution and its application to censored Data, Communication in Statistics-Theory and Methods, Vol. 36, pp. 1855–1866.

GHITANY, M. E., ATIEH, B., NADARAJAH, S., (2008). Lindley distribution and its application, Mathematics and Computers in Simulation, Vol. 78, pp. 493–506.

GRADSHTEYN, I. S., RYZHIK, I. M., (2000). Table of Integrals, Series, and Products, Academic Press, New York.

GROSS, A. J., CLARK, V. A., (1975). Survival Distributions: Reliability Applications in the Biomedical Sciences. John Wiley and Sons, New York.

GUPTA, GARG, M., MAHESH, G., (2016). The Lomax-Gumbel Distribution, Palestine Journal of Mathematics, Vol. 5(1), pp. 35–42.

HASSAN, A. S., AL-GHAMDI, A. S., (2009). Optimum step stress accelerated life testing for Lomax Distribution, Journal of Application in Scientific Research, Vol. 5, pp. 2153–2164.

HOWLADER, H. A., HOSSAIN, A. M., (2002). Bayesian Survival Estimation of Pareto Distribution of the second kind based on failure-censored data, Computational Statistics and Data Analysis, Vol. 38, pp. 301–314.

JONES, MC., (2004). Family of Distributions Arising from Distribution of Order Statistics, Test, Vol. 13, pp. 1–43.

KAWSAR, F., UZMA, J., AHMAD, S. P., (2108). Statistical Properties of Rayleigh Lomax distribution with applications in Survival Analysis, Journal of Data Science, Vol. 16(3), pp. 531–548.

LEE, E. T., WANG, J. W., (2003). Statistical Methods for Survival Data Analysis (3rd ed.). New York: Wiley.

LEMONTE, A. J., CORDEIRO, G. M., (2013). An extended Lomax distribution, Statistics, Vol. 47, pp. 800–816.

LINGAPPAIAH, G. S., (1986). On the Pareto Distribution of the second kind (Lomax Distribution). Revista de Mathemtica e Estatistica, Vol. 4, pp. 63–68.

LOMAX, K. S., (1954). Business failures: Another example of the analysis of failure data, Journal of American Statistical Association, Vol. 45, pp. 21–29.

MARSHALL, A. W., OLKIN, I., (1997). A new method for adding a parameter to a family of distributions with application to the Exponential and Weibull families, Biometrika, Vol. 84, pp. 641–652.

MYHRE, J., SAUNDERS, S., (1982). Screen testing and conditional probability of survival, In: Crowley, J. and Johnson, R.A., eds. Survival Analysis. Lecture Notes-Monograph Series, Institute of Mathematical Statistics, Vol. 2, pp. 166–178.

NAYAK, K. T., (1987). Multivariate Lomax Distribution: Properties and Usefulness in Reliability Theory, Journal of Applied Probability, Vol. 24, pp. 170–177.

OGUNTUNDE, P. E., KHALEEL, M. A., AHMED, M. T., ADEJUMO, A. O., ODETUNMIBI, O. A., (2017). A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate, Hindawi, Modelling and Simulation in Engineering, Vol. 2017, pp. 1–7.

TAHIR, M. H., CORDEIRO, G. M., MANSOOR, M., ZUBAIR, M., (2015). The Weibull Lomax distribution: properties and applications, Hacet J Math Stat, Vol. 44(2), pp. 461–480.

TAHIR, M. H., ADNAN HUSSAIN, M., CORDEIRO, G. M., HAMEDANI, G. G., MANSOOR, M., ZUBAIR, M., (2016). The Gumbel-Lomax distribution: properties and applications, Journal of Statistical Theory and Applications, Vol. 15(1), pp. 61– 79.

TERNA, G. I., DAVID, A. K., (2018). On the Properties and Applications of LomaxExponential Distribution, Asian Journal of Probability and Statistics, Vol. 1(4), pp.1–13.

VIDONDO, B., PRAIRIE, Y. T., BLANCO, J. M., DUARTE, C. M., (1997). Some Aspects of the Analysis of Size Spectra in Aquatic Ecology, Limnology and Oceanography, Vol. 42, pp. 84–192.

ZEA, L. M., SILVA, R. B., M. BOURGUIGNON, M., A. M. SANTOS, M. A., CORDEIRO, G. M., (2012). The beta exponentiated Pareto distribution with application to bladder cancer susceptibility, International Journal of Statistics and Probability, Vol. 1, pp. 8–19.

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