Properties and applications of beta Erlang-truncated exponential distribution

Volume 22, Issue 1, pp 16--37
Publication Date: June 05, 2020 Submission Date: February 03, 2019 Revision Date: February 26, 2020 Accteptance Date: April 08, 2020


M. Shrahili - Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia. I. Elbatal - Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia. - Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt. Isyaku Muhammad - Department of Mechanical Engineering, School of Technology, Kano State Polytechnic, Nigeria. Mustapha Muhammad - Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano (BUK), Nigeria.


In this article, we proposed a new four-parameter distribution called beta Erlang truncated exponential distribution (BETE). Some important mathematical and statistical properties of the proposed distribution are examined. The stochastic ordering result for the BETE was also discussed. Moreover, the \(r^{\rm th}\) moment, moment generating function, incomplete moments, mean deviations, Bonferroni and Lorenz curves, moments of residual life, Shannon and Renyi entropies, and Kullback--Leibler divergence measure are derived. The maximum-likelihood estimate for the unknown parameters of the BETE was established and assessed by the simulation studies. The maximum likelihood estimation of the stress-strength parameter is discussed and its asymptotic distribution is obtained. The effectiveness and usefulness of the BETE are demonstrated by the use of three real data set, in which the BETE provide a better fit than some other existing distributions and demonstrated its capability in the stress-strength reliability analysis.

Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

M. Shrahili, I. Elbatal, Isyaku Muhammad, Mustapha Muhammad, Properties and applications of beta Erlang-truncated exponential distribution, Journal of Mathematics and Computer Science, 22 (2021), no. 1, 16--37

AMA Style

Shrahili M., Elbatal I., Muhammad Isyaku, Muhammad Mustapha, Properties and applications of beta Erlang-truncated exponential distribution. J Math Comput SCI-JM. (2021); 22(1):16--37

Chicago/Turabian Style

Shrahili, M., Elbatal, I., Muhammad, Isyaku, Muhammad, Mustapha. "Properties and applications of beta Erlang-truncated exponential distribution." Journal of Mathematics and Computer Science, 22, no. 1 (2021): 16--37