Abstract
In this article, we propose four confidence intervals (CIs) for parameter estimation of the Kpenadidum distribution, which is applied in lifetime data analysis. We developed and evaluated different types of CIs, including likelihood-based, Wald-type, bootstrap- \(t\) , and bias-corrected accelerated bootstrap CIs. The comparison was conducted using a simulation study and an application with a real data set. These CIs were evaluated based on their empirical coverage probability (ECP) and average width (AW) across various situations. Furthermore, we derived the explicit formula for computing the Wald-type CI, which simplifies the computation. The results show that the ECPs of the likelihood-based and Wald-type CIs tend to converge toward the nominal confidence level of 0.95 in almost all situations. When the sample size is small ( \(n=10\) , 20, or 30), the bootstrap- \(t\) and BCa bootstrap CIs produce ECPs less than 0.95. As the sample sizes increase, the ECPs of the bootstrap- \(t\) and BCa bootstrap CIs tend to approach the nominal confidence level. Additionally, the parameter values impact the ECP. At low parameter values, the CPs are quite close to the nominal confidence level, with the likelihood-based and Wald-type CIs achieving an ECP of approximately 0.95. However, the ECPs for the bootstrap- \(t\) and BCa bootstrap CIs tend to have lower coverage at higher parameter values with small sample sizes. We confirmed the efficacy of the CIs by applying them to the monthly tax revenue in Egypt, and the results matched those from the simulation study.
