Type II general inverse exponential family of distributions

Abstract

In this paper, we introduce a new family of distributions based on the T-X transformation, the inverse exponential distribution, the odds function and the Lehmann type II distribution. We investigate its general mathematical properties, including moments, moment generating function, quantile function, entropies and order statistics. A statistical model is constructed from a special case of the family using the Bur III distribution (also known as exponentiated Lomax distribution) as baseline. The estimation of the parameters are performed by the maximum likelihood method and the least square method. Finally, we illustrate its importance by means of two applications to real life data sets.

Subject Classification (2000):

• 60E05
• 62E15
• 62F10

Keywords:

• T-X transformation
• Inverse exponential distribution
• Maximum likelihood estimation