Journal of Prime Research in Mathematics

# Modified beta generalized linear failure rate distribution: theory and applications

Farrukh Jamal
Department of Statistics, The Islamia University Bahawalpur, Pakistan.
Ibrahim Elbatal
Institute of Statistical Studies and Research (ISSR), Department of Mathematical Statistics, Cairo University, Egypt.
Christophe Chesneau$$^1$$
Department of Mathematics, LMNO, University of Caen-Normandie, Caen, France.

Mohammed Elgarhy
Department of Mathematics and Statistics, University of Jeddah, Jeddah, Kingdom of Saudi Arabia.
Amal S. Hassan
Institute of Statistical Studies and Research (ISSR), Department of Mathematical Statistics, Cairo University, Cairo.
$$^{1}$$Corresponding Author: christophe.chesneau@unicaen.fr

### Abstract

In this paper we introduce a new comprehensive six-parameter distribution called the modified beta generalized linear failure rate distribution. One of the interest of this distribution is to generalize some well-known flexible distributions discussed in the literature, such as (i) the beta linear failure rate distribution, (ii) the generalized linear failure rate distribution, (iii) the beta exponential distribution, (iv) the beta Rayleigh distribution and (v) the generalized exponential distribution, among others. We derive some of its statistical properties, including the moments, the moment generating function, the quantile function, the order statistics and the mean deviations. We propose the method of maximum likelihood for estimating the model parameters. A simulation study is performed in order to investigate the performance of the maximum likelihood estimators. A real data set is used to illustrate the importance and the flexibility of the new distribution.

#### Keywords:

Modified beta distribution, generalized linear failure rate distribution, moments, moment generating function, maximum likelihood estimation.