Confidence Intervals for the Zeghdoudi Distribution Parameter: Applications in Precipitation and COVID-19 Data Analysis

This paper proposes four confidence intervals (CIs) for estimating the parameters of the Zeghdoudi distribution, which is commonly used in the analysis of lifetime data. We introduce and evaluate the likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap CIs using Monte Carlo simulation studies and apply them to two real datasets. We assess the effectiveness of these CIs by evaluating their empirical coverage probability (CP) and average length (AL), which offer valuable insights into their performance in various scenarios. Furthermore, we have developed an explicit formulation of the Wald-type’s CI formula, simplifying its computation. The results demonstrate that the CPs of likelihood-based and Wald-type CIs converge towards the nominal confidence level of 0.95 for all cases. However, when the sample size is small, the bootstrap-t and BCa bootstrap CIs have CPs less than 0.95. On the other hand, as sample sizes increase, the CPs of all CIs tend to approach 0.95. However, when the sample sizes are small, the CPs of the bootstrap-t and BCa bootstrap CIs tend to decrease. We verified the efficacy of CIs by applying them to precipitation data and COVID-19 mortality rate data, and the results matched those from the simulation study.