This paper addresses the problem of fitting a known distribution function to the marginal distribution of a stationary long memory moving average random field observed on increasing ν-dimensional "cubic" domains when its mean µ and scale σ are known or unknown. Using two suitable estimators of µ and a classical estimate of σ, a modification of the Kolmogorov-Smirnov statistic is defined based on the residual empirical process and having a Cauchy-type limit distribution, independent of µ, σ and the long memory parameter d. Based on this result, a simple goodness-of-fit test for the marginal distribution is constructed, which does not require the estimation of d or any other underlying nuisance parameters. The result is new even for the case of time series, i.e., when ν = 1. Findings of a simulation study investigating the finite sample behavior of size and power of the proposed test is also included in this paper.
Constructing tests for exponentiality has been an active and fruitful research area, with numerous applications in engineering, biology and other sciences concerned with life-time data. In the present paper, we construct and investigate powerful tests for exponentiality based on two well known quantities: the Atkinson index and the Moran statistic. We provide an extensive study of the performance of the tests and compare them with those already available in the literature.
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