Confidence Intervals for the Ram Awadh Distribution Parameter: Applications in Engineering and COVID-19 Data

Abstract

In applied sciences and medical sciences, accurate estimation of distribution parameter is crucial for data analysis and decision-making. This study proposes various confidence interval (CI) estimation methods for the parameter of the Ram Awadh distribution, a distribution commonly used in reliability and lifetime data analysis. The methods evaluated include likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap CIs. Through extensive simulation studies, we compare the performance of these methods in terms of empirical coverage probability (ECP) and average length (AL) of the CIs under different sample sizes. Additionally, an explicit formulation of the CI formula for the Wald-type has been derived, simplifying its computation process. The results indicate that both likelihood-based and Wald-type methods consistently approach the nominal confidence level of 0.95 in all scenarios. However, with small sample sizes, the ECP of bootstrap-t and BCa bootstrap CIs tends to decrease. Conversely, as sample sizes increase, the ECPs of all CIs tend to converge towards 0.95. Moreover, for all methods, the AL of CIs substantially decreases with increasing sample size. To validate the efficacy of the CIs, they were applied to engineering and COVID-19 data, and the results aligned with those obtained from the simulation studies. In two real-world settings, this thorough evaluation shows that the proposed CIs are reliable and useful for accurately estimating the parameter of the Ram Awadh distribution.