Journal of Biostatistics & Biometrics

research article

On Modified Burr XII-Inverse Exponential Distribution: Properties, Characterizations and Applications

Fiaz Ahmad Bhatti1*, Gholamhossein Hamedani2, Haitham M. Yousof3, Azeem Ali1, Munir Ahmad1

1National College of Business Administration and Economics, Lahore, Pakistan

2Marquette University, Milwaukee, WI, USA

3Department of Statistics Mathematics and Insurance, Benha University, Al Qalyubia Governorate, Egypt

*Corresponding author: Fiaz Ahmad Bhatti, National College of Business Administration and Economics, Lahore, Pakistan. Email:

Received Date: 06 September, 2018; Accepted Date: 25 September, 2018; Published Date: 05 October, 2018



In this paper, a flexible lifetime distribution with increasing, increasing and decreasing and modified bathtub hazard rate called Modified Burr XII-Inverse Exponential (MBXII-IE) is introduced. The density function of MBXII-IE has exponential, left-skewed, right-skewed and symmetrical shapes. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The MBXII-IE distribution is characterized via different techniques. Parameters of MBXII-IE distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the MBXII-IE distribution. The potentiality of MBXII-IE distribution is demonstrated by its application to real data sets: fracture toughness, taxes revenue’s data and coal mining disaster data.

Keywords: Characterizations; Moments; Maximum Likelihood Estimation; Reliability