Kumaraswamy-Janardan Distribution: A Generalized Janardan Distribution with Application to Real Data
Nelson Doe Dzivor *
Department of Applied Mathematical and Statistics, Accra Technical University, Accra, Ghana.
Henry Otoo
Department of Mathematical Science, University of Mines and Technology, Tarkwa, Ghana.
Eric Neebo Wiah
Department of Mathematical Science, University of Mines and Technology, Tarkwa, Ghana.
*Author to whom correspondence should be addressed.
Abstract
The quest to improve on flexibility of probability distributions motivated this research. Four-parameter Janardan generalized distribution known as Kumaraswamy-Janardan distribution is proposed through method of parameterization and studied. The probability density function, cumulative density function, survival rate function as well as hazard rate function of the distribution are established. Statistical properties such as moments, moment generating function as well as maximum likelihood of the model are discussed. The parameters are estimated using the simulated annealing optimization algorithm. Flexibility of the model in comparison with the baseline model as well as other competing sub-models is verified using Akaike Information Criteria (AIC). The model is tested with real data and is proven to be more flexible in fitting real data than any of its sub-models considered.
Keywords: Janardan; Kumaraswamy, akaike information criteria, parameterization, moment generating function.