A NEW MODIFIED GENERALIZED ODD LOG-LOGISTIC DISTRIBUTION WITH THREE PARAMETERS

Abstract

Statistical distributions are very useful in describing and predicting real-world phenomena. Numerous extended distributions have been extensively used over the last decades for modeling data in many applied sciences such as medicine, engineering and finance. Recent developments focus on defining new families that extend well-known distributions and at the same time provide great flexibility in modeling data in practice. In this paper, we have introduced a new three-parameter exponential distribution called the generalized odd log-logistic-exponential distribution by using the generator defined by Cordeiro et al (2017). This model extends the odd log-logistic-exponential and exponential distributions. Several of its structural properties are discussed in detail. These include shape of the probability density function, hazard rate function, quantile function order statistics, and moments. The method of maximum likelihood is adopted to estimate the model parameters. The applicability of the new models is illustrated by using real data. The goodness-of-fits of the exponential, beta exponential, Kumaraswamy exponential and the generalized odd log-logistic-exponential distributions have been compared through the AIC, AICC, BIC and KS statistics and found that the generalized odd log-logistic-exponential distribution fits well the data.

Key Word: Exponential distribution, odd log logic distribution, maximum likelihood estimation, Monte Carlo.