Testing of Scale Parameter of the Exponential Distribution With Known Coefficient of Variation: Conditional Approach

Abstract

Tests of hypothesis of the parameter of the reduced exponential distribution E(a, ) has been studied from a conditional viewpoint, based on the conditionality principle of R. A. Fisher. It is shown that conditionally, optimal tests are possible though unconditionally no such test exists. Some desirable properties of the conditional test and large sample approximations to the upper percentile point of the conditional test statistic are also presented. The equivalence of two ancillaries for conditioning with respect to power criterion is shown.

Tests for Equality of Parameters of Two Exponential Distributions with Common Known Coefficient of Variation

“…The family of conditional densities of X i 1 given C i is scale family and has MLR w.r.t. parameter i (see Lemma 2, Handa et al, 2002).…”

“…We can thus hope to find optimal tests under conditional setup for one-sided hypothesis (1.2) using MLR when it exists. We extend the results of Handa et al (2002) to develop a one-sided UMP conditional test for hypothesis (1.2) in Sec. 3.…”

“…By using the conditional distributions of X i 1 given C i (see Lemma 2, Handa et al, 2002) and standard arguments, the pdf can be obtained after some simplifications in the form given below: f * /c 1 c 2 = n 1 /c 1 n 1 n 2 /c 2 n 2 J a * n 1 c 1 + n 2 c 2 * n 1 + n 2 * n 2 −1 J n 1 a/c 1 n 1 J n 2 a/c 2 n 2…”