مقایسه قدرت و مطالعه شبیه سازی آزمون تناسب خوبی

We give the results of a comprehensive simulation study of the power properties of prominent goodness-of-fit tests. For testing the normal N(μ,σ2), we propose a new omnibus goodness-of-fit statistic C which is a combination of the Shapiro–Wilk statistic W and the correlation statistic R. We show that the test of normality based on C is overall more powerful than other prominent goodness-of-fit tests and is effective against both symmetric as well as skew alternatives. We also show that the null distribution of C can be approximated by a four-moment F. For the exponential E(θ,σ), Tiku statistic Z (using sample spacings) and modified Anderson–Darling A are the most powerful. For testing other distributions, the statistics based on generalized sample spacings and the modified Anderson–Darling statistic provide the most powerful tests.

A parametric procedure usually hinges on the assumption of a particular distribution. It is, therefore, of utmost importance to assess the validity of the assumed distribution. This is accomplished by doing a goodness-of-fit test. A galaxy of omnibus goodness-of-fit tests are available; see, for example, [1] and the references in [2, Chapters 1–7]. In this paper, we report the simulation results for the tests we found to be overall most powerful: (i) the combined statistic C for testing normal N(μ,σ2), (ii) the statistics Z (using exponential sample spacings) and the modified Anderson–Darling statistic for testing exponential E(θ,σ), (iii) the statistic Z∗ (using generalized sample spacings) for testing a skew distribution, and for testing a symmetric distribution against skew alternatives, (iv) the modified Anderson–Darling statistic and the correlation statistic R for testing uniform View the MathML source. A four-moment approximation is available to the null distribution of C. The null distributions of Z∗ and U are effectively normal for all sample sizes n≥7 and their power functions can also be derived analytically. The tests based on the EDF statistics are generally difficult to implement since they involve parameter estimation. This work can be good material for software developers because it identifies the most powerful goodness-of-fit statistics and gives their approximate null distributions. The latter can be used for calculating p-values.