A new transmutation: conditional copula with exponential distribution

Abstract

In these days, many different techniques are implemented for generating distributions. The core aim in generating distribution, is better modeling capability. With generating new distribution more reliable and appropriate models are available for data sets. In this paper, a new distribution is gained by evaluating the conditional diagonal section of the bivariate Farlie-Gumbel-Morgenstern distribution with exponential marginals. Specifications and characteristics of this new distribution are studied. The statistical assessment and some reliability analyzes are carried out. The success of the new distribution on statistical modeling is detected by using data sets in literature. It is concluded that this new distribution suggests a model that can be used effectively in many different lifetime data sets.

Keywords

• Farlie-Gumbel-Morgenstern distribution
• copula
• reliability analysis
• generating distribution
• exponential distribution

References

1. Al-Mutairi, D. K., Ghitany, M. E., Kundu, D., Inferences on stress-strength reliability from Lindley distributions, Communications in Statistics, Theory and Methods, 42(8) (2013), 1443–1463, https://dx.doi.org/10.1080/03610926.2011.563011.
2. Alghamedi, A., Dey, S., Kumar, D., Dobbah, S. A., A new extension of extended exponential distribution with applications, Annals of Data Science, 7(1) (2020), 139–162, https://dx.doi.org/10.1007/s40745-020-00240-w.
3. Barreto-Souza, W., Bakouch, H. S., A new lifetime model with decreasing failure rate, Statistics, 47(2) (2013), 465–476, https://dx.doi.org/10.1080/02331888.2011.595489.
4. Devore, J. L., Probability and Statistics for Engineering and the Sciences, 8. ed., Internat. Student ed., Brooks/Cole, Cengage Learning, [Belmont, Calif. [u.a.]], 2012.
5. Dey, S., Ghosh, I., Kumar, D., Alpha-power transformed lindley distribution: Properties and associated inference with application to earthquake data, Sankhya, 73 (2011), 623–650, https://dx.doi.org/10.1007/s40745-018-0163-2.
6. Ghitany, M. E., Atieh, B., Nadarajah, S., Lindley distribution and its application, Mathematics and Computers in Simulation, 78(4) (2008), 493–506.
7. Linhart, H., Zucchini, W., Model Selection, John Wiley, 1986.
8. Nadarajah, S., Haghighi, F., An extension of the exponential distribution, Statistics, 45(6) (2011), 543–558, https://dx.doi.org/10.1080/02331881003678678.

9. Nelsen, R. B., An Introduction to Copulas, Second Edition, @Springer Series in Statistics, Springer Science+Business Media, Inc, New York, NY, 2006.
10. Rather, N. A., Rather, T. A., New generalizations of exponential distribution with applications, Journal of Probability and Statistics, 2017(2017), 1–9.
11. Ross, S. M., Introduction to Probability Models, Elsevier, 2010.
12. Shanker, R., Fesshaye, H., Selvaraj, S., On modeling of lifetimes data using exponential and lindley distributions, Biometrics & Biostatistics International Journal, 2(5) (2015), 1–9, https://dx.doi.org/10.15406/bbij.2015.02.00042.
13. Sklar, A., Fonctions de repartition an dimensionset leurs marges, Publ. Inst. Statis. Univ (1959), 229–231.
14. Ünözkan, H., Yilmaz, M., A new method for generating distributions: An application to flow data, International Journal of Statistics and Applications, 9(3) (2019), 92–99, https://dx.doi.org/10.5923/j.statistics.20190903.04.