Abstract
Abstract A generalized simple test function is proposed for testing a hypothesis on the location parameter of the exponential law, assuming its scale parameter to be unknown. The probability density function of such a test statistic is derived to compute critical values for specified levels of significance. Several moment-recurrence formulas of this test statistic are established which reveal interesting relationships between its rth and (r − 1)th order moments. Finally, its power function is also derived. The results applicable to the special cases of the generalized simple test function are mentioned and the useful properties of this test function in some special cases are pointed out. The general results of this paper include the results given in [1] and [2].
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