A Class of Exponential Rayleigh Distribution and New Modified Weighted Exponential Rayleigh Distribution with Statistical Properties

Lamyaa Khalid Hussein; Huda  Abdullah Rasheed; Iden  Hasan Hussein

doi:10.30526/36.2.3044

Authors

Lamyaa Khalid Hussein Department of Mathematics, College of Science, Mustansiriyah University
Huda Abdullah Rasheed Department of Mathematics, College of Science, Mustansiriyah University
Iden Hasan Hussein Department of Mathematic, College of Science for Women, University of Baghdad

DOI:

https://doi.org/10.30526/36.2.3044

Keywords:

Exponential Rayleigh (ER) distribution, Modified Weighted Exponential Rayleigh (MWER) distribution.

Abstract

This paper deals with the mathematical method for extracting the Exponential Rayleighh distribution based on mixed between the cumulative distribution function of Exponential distribution and the cumulative distribution function of Rayleigh distribution using an application (maximum), as well as derived different statistical properties for distribution, and present a structure of a new distribution based on a modified weighted version of Azzalini’s (1985) named Modified Weighted Exponential Rayleigh distribution such that this new distribution is generalization of the distribution and provide some special models of the distribution, as well as derived different statistical properties for distribution

References

Rayleigh, J. W. S. On the Resultant of a Large Number of Vibrations of the Some Pitch and of Arbitrary Phase, Philosophical Magazine Series, 1880,10, 60, 73 – 78.

Rahiem, N, A.; J., S. H.; Kalaf B. A. Estimate the Scale Parameter of Exponential Distribution Via Modified Two Stage Shrinkage Technique. Journal of College of Education, 2010, (6).

Fatima, K. ;Ahmad, S. Statistical Properties of Exponential Rayleigh Distribution and its Applications to Medical Science and Engineering, International Conference on Recent Innovations in Science, Agriculture, Engineering and Management 2017, 491 – 506.

Tahir, M; Aslam, M. Hussain, Z. ; Abbas, N. On the Finite Mixture of Exponential, Rayleigh and Burr Type-XII Distributions: Estimation of Parameters in Bayesian Framework, Electronic Journal of Applied Statistical Analysis, 2017,10, Issue 01, 271 – 293.

Isaac, R S.; Mehta, N. B. ; Ieee, S. M. Efﬁcient Computation of Multivariate Rayleigh and Exponential Distributions, IEEE Wireless Communications Letters, 2019,8, 2, 456 – 459.

Mohammed, M. J. ; Hussein, I. H. Study of New Mixture Distribution, Journal of Engineering and Applied Sciences, 2019,14, 20, 7566 – 7573.

Shi, X; Oluyede, B. O. ; Pararai, M. Theoretical Properties of Weighted Generalized Rayleigh and Related Distribution, Theoretical Mathematics & Applications, 2012, 2, 2, 45 – 62.

Oguntunde, P. E; Balogun, O. S; Okagbue, H. I. ; Bishop, S. A. The Weibull-Exponential Distribution: Its Properties and Applications, Journal of Applied Sciences, 2015,15,11, 1305 – 1311.

Merovci, F. ; Elbatal, I. Weibull Rayleigh Distribution: Theory and Applications, Applied Mathematics and Information Sciences, 2015,9, 4, 2127 – 2137

Nasiru, S. Another Weighted Weibull Distribution from Azzalini’s Family, European Scientific Journal March, 2015,11, 9, 134 – 144.

Hussian, M. A. A Weighted Inverted Exponential Distribution, International Journal of Advanced Statistics and Probability, 2013,1, 3, 142 – 150.

Oguntunde, P E; Owoloko, E. A. ; Balogun, O. S. On A New Weighted Exponential Distribution: Theory and Application, Asian Journal of Applied Sciences, 2016,9, 1, 1 – 12.