Abstract
In this article, we have presented some of the asymptotic distributions related to two one (left or right) – truncation parameter family of distributions. The asymptotic conditional distribution of complete sufficient statistic of parameter of interest is obtained by conditioning the distribution of complete sufficient statistic of nuisance parameter to be held fixed. Using this conditional distribution we have derived asymptotic uniformly most powerful invariant tests for testing hypotheses (i) one parameter is larger than the other and (ii) the equality of the truncation parameters of two independent one (left or right) – truncation parameter family of distributions. Attempt has also been made to calculate the power and to draw the corresponding power curve. A comparative study has been done with the likelihood ratio test.
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