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

Year 2017, Volume: 30 Issue: 2, 219 - 236, 19.06.2017

Omid Kharazmi Leila Jabbari

Abstract

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 ,

References

• 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.