A new two-parameter distribution: properties and applications

Document Type: Research Paper


1 Department of Statistics, Islamic Azad University, Tehran north branch, Tehran, Iran

2 Department of Statistics, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran

3 Department of Statistics, Bartin University, Bartin 74100, Turkey


In this paper, a new two-parameter lifetime distribution called ``the exponentiated Shanker distribution" is suggested. The new distribution has an increasing, decreasing and bathtub-shaped hazard rate function (hrf) for modeling lifetime data. Various mathematical and statistical properties of the proposed distribution including its hrf, complete and incomplete moments, skewness and kurtosis, mean deviations, Bonferroni and Lorenz curves are discussed. Estimation of its parameters is also discussed using the method of maximum likelihood estimation and a simulation study is given. Finally, two applications of the new distribution are presented using two real data sets. The results also confirmed the suitability of the proposed model for the real data sets.