A Novel flexible Probability Model for Improved Model Adequacy: Its Properties and Applications

Abstract In the current decade development of new distributions is a frequently used practice in probability theory. In this manuscript, we introduce a novel probability distribution which is referred as “Alpha Power Modified Inverse Rayleigh (APMIR) distribution”. Some important statistical properties of the suggested model have been derived and investigated thoroughly. These properties include higher order moments, Shannon and Renyi entropy, order statistics, mode etc. The maximum likelihood estimation (MLE) procedure is used to obtain estimates of the parameters of the suggested distribution. The performance of the proposed model is assessed using two real data sets. Simulation results are conducted to evaluate and justify the consistency of MLE. The suggested model offers better presentation as compared to other kinds of Rayleigh model.