This is a preview and has not been published.

Properties and Applications of the Type I Half-logistic Nadarajah-Haghighi Distribution


  • M. Shrahili
  • Mustapha Muhammad
  • I. Elbatal
  • Isyaku Muhammad
  • Mouna Bouchane
  • Badamasi Abba


A new three-parameter distribution called the type I half-logistic Nadarajah-Haghighi (T IHL N H ) is proposed. We discussed some important mathematical and statistical properties of the new model such as an explicit form of its r th moment, mean deviations,
quantile function, Bonferroni and Lorenz curves. The Shannon entropy and Renyi entropy are computed, the expression for the Kullback-Leibler divergence measure is provided. The model parameters estimation was approached by the maximum likelihood
estimation (MLE), and the information matrix is obtained. The finite sample properties of the MLEs are investigated numerically by simulation studies; by examining the bias and mean square error of the estimators, and the results was satisfactory. We used two
real data applications to demonstrate the superior performance of the T IHL N H in terms of fit over some other existing lifetime models.


M. Shrahili

Department of Statistics and Operations Research
College of Science, King Saud University

Associate Professor.

I. Elbatal

1. Department of Mathematics and Statistics, College of Science,
Imam Mohammad Ibn Saud Islamic University (IMSIU)
2. Faculty of Graduate Studies for Statistical Research,
Cairo University, Egypt.


Isyaku Muhammad

Department of Mechanical Engineering,
School of Technology, Kano State Polytechnic.


Mouna Bouchane

Key Laboratory of Augmented Reality,
College of Mathematics and Information Science,
Hebei Normal University.

Ph.D. students. 



How to Cite

Shrahili, M., Muhammad, M. ., Elbatal, I., Muhammad, . . . I., Bouchane, M. ., & Abba, B. Properties and Applications of the Type I Half-logistic Nadarajah-Haghighi Distribution. Austrian Journal of Statistics, 52(2), 1–21. Retrieved from