A weighted inverted exponential distributions
Abstract
In this paper, a generalized version of the inverted exponential distribution called the weighted inverted exponential distribution is introduced. The proposed distribution is used to analyze lifetime data. Several statistical properties of the weighted inverted exponential distribution are studied and derived. Least squares estimation, maximum likelihood estimation and Bayesian estimation methods are used to evaluate the distribution parameters. Numerical simulation and a real-life data analysis are carried out to validate the robustness of the proposed distribution.
About this article
References
Fisher, R.A.: The effects of methods of ascertainment upon the estimation of frequencies. Ann. Human Genet. 6(1), 439–444 (1934)
Cox, D.R.: Renewal Theory. Barnes & Noble, New York (1962)
Zelen, M.: Problems in cell kinetics and early detection of disease. Reliab. Biometry 56(3), 701–726 (1974)
R. D. Gupta and D. Kundu, “A new class of weighted exponential distributions”, Statistics, vol. 43, no. 6, pp. 621 - 634, 2009.
A. Azzalini, “A class of distributions which includes the normal ones”, Scandinavian Journal of Statistics, vol. 12, pp. 171 - 178, 1985
View more references (14)
M. K. Shakhatreh, “A two-parameter of weighted exponential distributions”, Statistics & Probability Letters, vol. 82, no. 2, pp. 252 - 261, 2012.
M. M. Ramadan. “A Class of Weighted Weibull Distributions and Its Properties”, CSCanda, Studies in Mathematical Sciences Vol. 6, No. 1, , pp. 35 – 45, 2013.
M. Q. Shahbaz, N. S. Shahbaz and N. S. Butt, “A Class of Weighted Weibull Distribution”, Pak.j.stat.oper.res. Vol. VI, No. 1, pp. 53-59, 2010.
A.Z. Killer and A. R. Kamath, “Reliability analysis of CNC Machine Tools”, Relieb. Engng., vol. 3, pp. 449 - 473, 1982.
C. T. Lin, B. S. Duran and T. O. Lewis, “Inverted gamma as life distribution”, Microelectron Reliab., vol. 29, no. 4, pp. 619 - 626, 1989.
A. M. Abouammoh and A. M. Alshingiti, “Reliability estimation of Generalized inverted exponential distribution”, J. Statist. Comput. Simul., vol. 79, no. 11, pp. 1301 - 1315, 2009
M. C. Jones, “Families of distributions arising from distributions of order statistics”, Test, vol. 13, pp. 1 - 43, 2004.
S. Nadarajah and S. Kotz, “A f1-beta distribution”, Braz. J. Probab. Stat., vol. 20, no. 1, 13 - 27. 2006
R. E. Barlow and F. Proschan, “Importance of system components and fault tree events”, Stochastic Process. Appl., vol. 3, pp. 153 - 173, 1975.
N. Ebrahimi, “How to measure uncertainty in the residual lifetime distribution”, Sankhya Ser. A, vol. 58, pp. 48 - 56, 1996.
A. Belkacem and B. Alexandre, “Mean residual life estimation”, Journal of Statistical Planning and Inference, vol. 132, pp. 3 - 19, 2005
S. Karlin, “Total Positivity, vol. 1.”, Stanford University press, Stanford, 1968.
A. Gelman, , J. B. Carlin, H. S. Stern, and D. B. Rubin, “Bayesian Data Analysis, Second Edition”, Chapman & Hall/CRC, New York, 2004.
R. C. Gupta and H. O. Akman, “On the reliability studies of a weighted inverse Gaussian model”. Journal of Statistical Planning and Inference, vol. 48, pp. 69 - 83, 1995.