Testing Lognormal and Exponential Distributions: Estimation of Percentile Points

SYNOPTIC ABSTRACT

Two tables of percentiles of the asymptotic test statistics of separate families of hypotheses proposed by D. R. Cox are presented. The symmetrical probability levels of α at 0.025, 0.25, 0.50, 0.75, and 0.975 are evaluated for various selected sample sizes. Three different methods for approximating these selected percentiles are compared. A comparison for small sample sizes is also presented. 95% confidence intervals are given for each of the percentile points estimated by the three methods. These results can be used for testing hypotheses involving lognormal and exponential distributions.

Key Words and Phrases:

• lognormal and exponential distributions
• 19-point formula
• separate families
• percentile points
• Cornish-Fisher
• Bowman-Shenton
• confidence intervals