On a Sum and Difference of Two Quasi Lindley Distributions: Theory and Applications

Yasser M. Amer^1, , Dina H. Abdel Hady² and Rania M. Shalabi³

¹Cairo Higher Institutes in Mokattam, Cairo, Egypt

²Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Tanta University, Egypt

³The Higher Institute of Managerial Science, 6th of October, Giza, Egypt

Cite this paper

Yasser M. Amer, Dina H. Abdel Hady and Rania M. Shalabi. On a Sum and Difference of Two Quasi Lindley Distributions: Theory and Applications. American Journal of Applied Mathematics and Statistics. 2021; 9(1):12-23. doi: 10.12691/AJAMS-9-1-3

Abstract

In this paper two basic random variables constructed from Quasi Lindley distribution have been introduced. One of these variables is defined as the sum of two independent random variables following the Quasi-Lindley distribution with the same parameter (2SQLindley). The second one is defined as the difference of two independent random variables following the Quasi-Lindley distribution with also the same parameter (2DQLindley). For both cases, we provided some statistical properties such as moments, incomplete moments and characteristic function. The parameters are estimated by maximum likelihood method. From simulation studies, the performance of the maximum likelihood estimators has been assessed. The usefulness of the corresponding models is proved using goodness-of-fit tests based on different real datasets. The new models provide consistently better fit than some classical models used in this research.

Keywords

Quasi Lindley distribution, mixed distribution, maximum likelihood estimation, incomplete moments, characteristic function, stochastic ordering and extreme order statistics

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Lindley, D. V. (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society. Series B. (Methodological). 20, 102-107.
[2]	Ghitany, M.E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its Applications, Mathematical Computation and Simulation, 78 (4), 493-506.
[3]	Zakerzadeh, H. and Dolati, A. (2009). Generalized Lindley distribution, Journal of mathematical extension. 3(2), 13-25.
[4]	Mahmoudi, E. and Zakerzadeh, H. (2010). Generalized Poisson-Lindley distribution, Communications in Statistics - Theory and Methods, 39 (10), 1785-1798.
[5]	Nadarajah, S., Bakouch, H.S. and Tahmasbi, R. (2011). A generalized Lindley distribution, Sankhya B-Applied and Interdisciplinary Statistics. 73, 331-359.
[6]	Zakerzadeh, H. and Mahmoudi, E. (2012). A New Two Parameter Lifetime Distribution: Model and Properties, arXiv:1204.4248 [stat.CO], http://arxiv.org/abs/1204.4248.
[7]	Ghitany, M.E., Al-Mutairi, D.K, Balakrishnan, N. and Al-Enezi, L.J. (2013). Power lindley distribution and associated inference, Computational Statistics and Data Analysis, 64, 20-33.
[8]	Shanker, R. and Mishra, A. (2013a). A two-parameter Lindley distribution, Statistics in transition new series, 14(1), 45-56.
[9]	Shanker, R. and Mishra, A. (2013b). A quasi Lindley distribution, African Journal of Mathematics and Computer Science Research. 6(4), 64-71.
[10]	Merovci, F. and Elbatal, I. (2014). Transmuted Lindley-geometric distribution and its applications, Journal of Statistics Applications and Probability. 3, 77-91.
[11]	Merovci, F. and Sharma, V.K. (2014). The beta Lindley distribution: Properties and applications, Journal of applied mathematics, 2014, Article ID 198951.
[12]	Tomy, L. (2018). A retrospective study on Lindley distribution, Biometrics and Biostatistics International Journal. 7(3), 163-169.
[13]	Thomas S.P., Jose K.K. and Tomy, L. (2019). Discrete Harris Extended Lindley Distribution and Applications, preprint.
[14]	Chesneau, C., Tomy, L. and Gillariose, J. (2019). A new modified Lindley distribution with properties and applications, preprint.
[15]	Chesneau. C, Tomy. L and Gillariose. J, (2020), On a Sum and Difference of two Lindley distributions: theory and applications, Revstat, 18 (5), 673-695.
[16]	Kotz, S., Kozubowski, T.J. and Podgorski, K. (2001). The Laplace Distribution and Generalizations. A Revisit with Applications to Communications, Economics, Engineering and Finance. Boston: Birkhäuser.
[17]	Bonferroni, C.E. (1930), Elementi di Statistca generale, Seeber, Firenze.
[18]	Leadbetter, M.R., Lindgren, G. and Rootzén H. (1987). Extremes and related properties of random sequences and processes. New York, Springer Verlag.
[19]	Bjerkedal T. (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. Am J Hyg, 72, 130-148.
[20]	Montgomery, D.C., Peck, E.A. and Vining, G.G. (2015). Introduction to Linear Regression Analysis, John Wiley and Sons.