Testing an assumed distribution

Abstract

<p>Testing for an assumed distribution has been a major area of statistical research, both in theory and in practice. A reason for this interest is that many statistical procedures are based on certain distributional assumptions. Two new statistics, BN and BL, are suggested in this thesis for testing for normal and logistic distributions. The formulation of these statistics is based on the best linear unbiased estimator of the population scale parameter δ, using order statistics. The distributions of BN and BL tend to normal very rapidly, effectively for sample size n ≥ 20. In general, BN and BL have good power properties. They are particularly sensitive in testing against skew distributions or symmetric distributions with large kurtosis. The power of BN is comparable with other available test-statistics.</p>