A new distribution model with two-parameter

Abstract

This paper deals with a two-parameter new mix distribution called as RL (Rayleigh- Logarithmic) distribution with increasing failure rate. Firstly, probability density function, distribution function, r th moment, survival and hazard functions of this two-parameter RL distribution are examined. Then, estimation of parameters by using standard statistical techniques such as maximum likelihood method and entropy are given for the new mix model. In the application part, a real data set is receipted and when RL distribution compared with other distributions, this RL distribution is shown be a good competitor.

Keywords

• Logarithmic distribution,maximum likelihood,Hazard function,Mix distribution

References

1. Lewin, L. Polylogarithms and Associated Functions, North Holland Amsterdam, 1981.
2. Adamidis, K., Loukas, S. A mix Distributions with Decreasing Failure Rate, Statist. Probab. Lett., 39, 35-42, 1998.
3. Tugrul, O.R. Energy sector and wind energy Potential in Turkey, Renewable Sustainable Energy Rev., 7, 469-484, 2003.
4. Ross, S.M., Shanthıkumar, J.G., Zhu, Z. On Increasing-Failure-Rate Random Variables, J. Appl. Prob., 42, 797- 809, 2005.
5. Lariviere, M. A Note on Probability Distributions with Increasing Generalized Failure Rates, Operations Research, 54/3, 602-604, 2006.
6. Kus, C. A New Lifetime Distribution, Comput. Statist. Data Anal., 51, 4497-4509, 2007.
7. Eskin, N., Artar, H., Tolun, S. Wind Energy Potential of Gokceada Island in Turkey, Renewable Sustainable Energy Rev. 12, 839-851, 2008.
8. Brusset, X. Properties of Distributions with Increasing Failure Rate, Munich Personal RePEc Archive, 2009.

9. Gupta, R.D., Kundu, D. A New Class of Weighted Exponential Distributions, Statistics, 43, 621-634, 2009.
10. Cancho, V.G., Louzada-Neto, F., Barriga, G.D.C. The Poissson- Exponential Mix Distributions, Comput. Stat. Data Anal., 55, 677-686, 2011.
11. Lu, W., Shi, D. A New Compounding Life Distribution: The Weibull-Poisson Distribution, J. of Appl. Stat., DOI:10.1080/02664763.2011.575126, 2011.
12. Silva, R.B., Cordeiro, G.M. The Burr XII Power Series Distributions: A New Compounding Family, Brazilian J. of Prob. and Stat., 29(3), 2013.
13. Bakouch, H.S., Jazi, M.A., Nadarajah, S., Dolati, A. A Lifetime Model with Increasing Failure Rate, Applied Mathematical Modelling, 38, 5392-5406, 2014.
14. Dey,S., Dey, T. Statistical Inference for the Rayleigh Distribution under Progressively Type II Censoring with Binomial Removal, Applied Mathematical Modelling, 38, 974-982, 2014.