Truncated exponentiated-exponential distribution: A distribution for unit interval

Abstract

A new distribution for the unit interval is defined. This distribution can be inflated in 1’s, thus being superior to the beta and Kumaraswamy distributions. Analytical expressions for the mode, quantile function, ordinary moments, incomplete moments and Rényi entropy are described. The generation of random numbers can be done easily. The estimation of the parameters is done by maximum likelihood. To validate the accuracy of the maximum likelihood estimator, Monte Carlo simulation studies are performed. Application to real data has shown that the new model is better than other well-known distributions.

Subject Classification: (2010):

• 46N30
• 46N40
• 97K80
• 54C70

Keywords:

• Truncated exponentiated-exponential distribution
• Random numbers
• Moments
• Monte Carlo simulation
• Unit interval
• Rényi entropy