Omid Kharazmi, Leila Jabbari
827 300


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.   


Weighted exponential distribution, Censored data, Simulation, Reliability,

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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


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.