Abstract Title

COMPARISON OF FREQUENTIST AND BAYESIAN TOLERANCE INTERVALS VIA SIMULATION

Presenter Name

Shivani Arora

Purpose (a):

To compare via simulations frequentist and Bayesian methods for estimating the shape parameter of a gamma distribution and apply the estimates to construct gamma tolerance interval.

Methods (b):

We generated data for various sample sizes (10, 20, 50 and 100) from gamma distribution with shape parameter = 0.25 to 7 (with an increment of 0.25). The scale parameter was held constant at 1. We obtained parameter estimate for the shape parameter via maximum likelihood method, method of moments and Bayesian approach. Next, we constructed 95% tolerance interval separately using each of the parameter estimates and evaluated the coverage probability.

Results (c):

All three methods failed to consistently provide 95% coverage. The coverage probability for the Bayesian approach was closer to 95% compared to the other two methods. For sample size less than 20, the coverage was close to 95% for the Bayesian approach and the method becomes progressively conservative when sample size becomes larger. This was observed consistently for all values of the shape parameter.

Conclusions (d):

Tolerance intervals are frequently used in environmental monitoring programs. Most monitoring programs for groundwater use samples of size 8 or 20 and our study shows that the Bayesian approach performs adequately for sample sizes less than 20.

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COMPARISON OF FREQUENTIST AND BAYESIAN TOLERANCE INTERVALS VIA SIMULATION