Convergence Analysis Of Two-Sided Tolerance Intervals For Weibull And Laplace Distributions: A Simulation Study

Abstract

There are unique difficulties in building two-sided tolerance intervals (TIs), particularly for some continuous distributions. The development and analysis of two-sided TIs for the Weibull and Laplace distributions are the main topics of this paper. These intervals are largely formed by maximum likelihood estimation (MLE); nevertheless, for certain distributions, MLE computations necessitate numerical solutions since closed-form equations are not available. In these situations, MLEs were successfully approximated using the Newton-Raphson approach. For two-sided TIs, coverage probabilities were assessed and recorded for a range of sample sizes and confidence/proportion pairs. The results showed that while the Weibull distribution needed larger sample sizes to reach comparable stability, the Laplace distribution showed comparatively faster convergence to nominal coverage levels. These findings offer insightful information about the design and functionality of TIs for various distributions, which guides their use in a variety of statistical scenarios