CONFIDENCE INTERVALS FOR THE PARAMETER OF THE IWUEZE DISTRIBUTION WITH APPLICATIONS TO MEDICAL AND ENGINEERING DATA.
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| Title: | CONFIDENCE INTERVALS FOR THE PARAMETER OF THE IWUEZE DISTRIBUTION WITH APPLICATIONS TO MEDICAL AND ENGINEERING DATA. |
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| Authors: | Wararit Panichkitkosolkul1,2 wararit@mathstat.sci.tu.ac.th |
| Source: | Reliability: Theory & Applications. Jun2024, Vol. 19 Issue 2, p526-543. 18p. |
| Subjects: | Confidence intervals, Engineering databases, Gamma distributions |
| Abstract: | One of the lifetime distributions is the Iwueze distribution, which is constructed by combining the exponential and gamma distributions. In this paper, confidence intervals (CIs) are proposed for the parameter of the Iwueze distribution using the likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap methods. We evaluated the performance of the proposed CI methods through Monte Carlo simulation in terms of their coverage probability (CP) and average length (AL) in various scenarios. Furthermore, we had also derived the explicit formula for the Wald-type CI, which is straightforward for computation. The simulation results showed that the likelihood-based and Wald-type CIs returned satisfactory results according to coverage probabilities, even for the setting of small sample sizes. On the other hand, both the bootstrap-t and BCa bootstrap CIs yield CPs lower than the nominal confidence level when sample sizes are small. However, as the sample sizes increase, the CP of all CIs tend to approach the nominal confidence level. The parameter values also have a minor influence on the CP of all CIs when the sample size is fixed. Moreover, the AL of all CIs decreases as the sample size increases. The Wald-type and likelihood-based CIs have very similar ALs for all parameter values. In general, the bootstrap-t CI tends to yield the shortest interval. The effectiveness of all CIs was demonstrated by applying them to medical and engineering data, yielding results consistent with those of the simulation study. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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