Arthritis is the tenderness and swelling of one or more of the joints. Arthritis therapies are directed mainly at reducing symptoms and improving quality of life. In this article, we introduced a novel four parametric model known as generalized exponentiated unit Gompertz (GEUG) for modeling a clinical trial data which represent the relief or relaxing times of arthritic patients receiving a fixed dosage of certain medication. The key feature of such novel model is the addition of new tuning parameters to unit Gompertz (UG) with the intention of increasing versatility of the UG model. We have derived and studied different statistical and reliable attributes, along with moments and associated measures, uncertainty measures, moments generating functions, complete/incomplete moments, quantile function, survival and hazard functions. A comprehensive simulation analysis is implemented to evaluate the effectiveness of estimation of distribution parameters using numerous well-known classical approaches, like maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson Darling estimation (ADE), right tail Anderson darling estimation (RTADE), and Cramer-Von Mises estimation (CVME). Finally, using a relief time's data on arthritis pain show adaptability of suggested model. The results revealed that it might fit better than other relative models.