Abstract:
In this paper, new goodness-of-fit tests are developed for the family of exponential distributions and for the Rayleigh distribution family with an arbitrary scale parameter, based on the difference of empirical Laplace transforms of a certain special property. Their limiting distributions and large deviation probabilities are described, the local Bahadur efficiency for natural alternatives is calculated, and an asymptotic comparison of the tests is performed. For the Rayleigh distribution family, the constructed test statistics are simulated, and their power is evaluated through statistical modeling for close alternative distributions.
Key words and phrases:exponential distribution, Rayleigh distribution, $U$-statistics, Bahadur efficiency, Large deviations, Kullback–Liebler information.
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