A NEW WEIGHTED EXPONENTIAL DISTRIBUTION AND ITS APPLICATION TO THE COMPLETE AND CENSORED DATA

The class of weighted exponential (WE) distribution was introduced in the seminal paper by Gupta and Kundu (2009) and have received a great deal of attention in recent years. In the present paper, we define a ﬂexible extension of the weighted exponential distribution called new weighted exponential (NEW) distribution. Various structural properties including statistical and reliability measures of the new distribution are derived. The method of maximum likelihood is used to estimate the parameters of the distribution in complete and censored setting. A simulation study is conducted to examine the bias and mean square error of the maximum likelihood estimators. Finally, two real data sets have been analyzed for illustrative purposes and it is observed that in both cases the proposed model ﬁts better than Weibull, gamma, weighted exponential, two-parameter weighted exponential, log-logistic , generalized exponential and generalized Weibull distributions.

Keywords:

Weighted exponential distribution, Censored data, Simulation Reliability, ,

PDF

___

Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on
Reliability, 36(1), 106-108.
Arnold, B. C., Balakrishnan, N., & Nagaraja, H. N. (1992). A first course in order
statistics (Vol. 54). Siam.
Arnold, B. C., & Beaver, R. J. (2000). Hidden truncation models. Sankhyā: The Indian
Journal of Statistics, Series A, 23-35.
Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian
Journal of Statistics 12:171–178.
Bjerkedal, T. (1960). Acquisition of Resistance in Guinea Pies infected with Different Doses
of Virulent Tubercle Bacilli. American Journal of Hygiene, 72(1), 130-48.
Glaser, R. E. (1980). Bathtub and related failure rate characterizations. Journal of the
American Statistical Association, 75(371), 667-672.
Ghitany, M. E., Aboukhamseen, S. M., & Mohammad, E. A. S. (2016). Weighted Half
Exponential Power Distribution and Associated Inference. Applied Mathematical
Sciences, 10(2), 91-108.
Gupta, R. D., Kundu, D. (2009). A new class of weighted exponential distributions. Statistics
:621–634.
Hosmer Jr, D. W., & Lemeshow, S. (1999). Applied survival analysis: Regression modelling
of time to event data. John Wiley& Sons, New York.
Kharazmi, O., Mahdavi, A., & Fathizadeh, M. (2015). Generalized Weighted Exponential
Distribution. Communications in Statistics-Simulation and Computation, 44(6), 1557-1569.
Klein, J. P., & Moeschberger, M. L. (2003). Survival analysis: statistical methods for
censored and truncated data. Springer-Verlag, New York, NY.
Renyi, A. (1961). On measures of entropy and information, in proceedings of the 4 th
berkeley symposium on Mathematical Statistics and Probability, 1, 547–561.
Shakhatreh, M. K. (2012). A two-parameter of weighted exponential distributions. Statistics
& Probability Letters, 82(2), 252-261.
Shaked, M., Shanthikumar, J. G. (2007). Stochastic Orders. Springer Verlag: New York.
Shannon, C. E. (1948). A mathematical theory of communication, bell System technical
Journal 27: 379-423 and 623–656. Mathematical Reviews (MathSciNet): MR10, 133e.

Gazi University Journal of Science-Cover

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1988
Yayıncı: Gazi Üniversitesi, Fen Bilimleri Enstitüsü

Arşiv