Modeling Time-to-Pain-Relief of Analgesic Drug: A Three-Shape-Parameter Modified Exponential Distribution Approach

In this study, the three-shape parameter modified exponential, also called the Kumaraswamy Modified Fréchet Exponential, is developed to ‎model time to pain relief. Some important properties of this new model are derived: These include the moments, moment generating function, ‎inequality measures, and mean residual life. The parameter estimates are computed under the maximum likelihood estimator. A simulation study ‎is carried out to investigate the behavior of parameters under the maximum likelihood estimation method. The quantile function is used to generate random numbers for the simulation study. We applied the Monte-Carlo simulation technique. The results show that the parameters with ‎their average bias (AB) and root mean square error (RMSE) decreased alongside increasing sample sizes: 50, 150, 250, 500, and 1000. ‎The results show that the three-shape parameter modified exponential behaves well with the maximum likelihood estimator. The three-‎shape parameter modified exponential model is applied to time-to-pain relief data of patients who received analgesic (pain killer medication). ‎Smaller Akaike and Bayesian Information criteria values are achieved better than all the competitive models; thus, the three-shape parameter ‎modified exponential model demonstrates a better fit for the data used‎.