Confidence Intervals for Common Mean of Delta-Lognormal Distributions Based on Left-Censored Data with Application to Rainfall Data in Thailand
Keywords:
Common mean, confidence interval, delta-lognormal distribution, left-censored data, rainfall dataAbstract
In environmental data analysis, it is common to encounter left-censored data, such as rainfall and particulate matter data, which follow the delta-lognormal distribution. This paper focuses on estimating confidence intervals for the common mean of delta-lognormal distributions based on left-censored data. The confidence intervals are constructed using four approaches: the generalized confidence interval approach, the Bayesian approach, the parametric bootstrap approach, and the adjusted method of variance estimates recovery approach. The performance of these approaches is evaluated through Monte Carlo simulations using RStudio programming. The results reveal that for the number of sample cases k = 3, the generalized confidence interval approach and the adjusted method of variance estimates recovery approach performed very well when the sample sizes were small, whereas the Bayesian approach performed exceptionally well for moderate and large sample sizes. For the number of sample cases k = 6, the generalized confidence interval approach and the adjusted method of variance estimates recovery approach performed very well for small and moderate sample sizes, while the Bayesian approach excelled for large sample sizes. The results are illustrated with rainfall data from three regions of Thailand.
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