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If one wants to test the hypothesis as to whether a set of observations comes from a completely specified continuous distribution or not, one can use the Kuiper test. But if one or more parameters have to be estimated, the standard tables for the Kuiper test are no longer valid. This paper presents a table to use with the Kuiper statistic for testing whether a sample comes from a normal distribution when the mean and variance are to be estimated from the sample. The critical points are obtained by means of Monte-Carlo calculation; the power of the test is estimated by simulation; and the results of the powers for several alternative distributions are compared with the estimated powers of the Kolmogorov-Smirnov test.In economic research, one often introduces an assumption about the form of the probability distribution from which a given set of observations is considered to be a random sample. For example, in the general linear model, one usually assumes that the disturbances are independently and normally distributed with zero mean and variance 6'. Such an assumption is of great importance because, in many cases, it determines the method that ought to be used to estimate the unknown parameters in the model and, furthermore, it determines the test procedures which the research worker may apply in the course of his study. Therefore, such a hypothesis influences the interpretation of the final results even though, in many economic studies, it assumes the character of a maintained hypothesis.There are several tests available for testing such an important assumption, that is, for determining whether a given sample comes from a completely specified distribution. The chi-square, the Kolmogorov-Smirnov, and the Kuiper tests are well-known examples. Hence, there is a problem of choice: which one should be used? The Kolmogorov-Smirnov and Kuiper tests are recommended where one is dealing with small sample sizes. As econometricians, this is important, because we usually have only small samples at our disposal. Furthermore, PEARSON [5] has came to the conclusion, after comparing several tests for goodness of fit, that the Kuiper test "seems to be a very good buy".The probability distribution of the Kolmogorov-Smirnov and Kuiper test statistics are both independent of the completely specified distribution function F(x) as postulated by the null hypothesis. The critical points of the former have been tabulated in [4] and those of the latter in [6].

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In earlier work (van Dijk, 1984, Chapter 3) one of the authors discussed the use of Monte Carlo integration methods for the computation of the multivariate integrals that are defined in the posterior moments and densities of the parameters of interest of econometric models. In the present paper we describe the computational steps of one Monte Carlo method, which is known in the literature as importance sampling. Further, a set of standard programs is available, which may be used for the implementation of a simple case of importance sampling. The computer programs have been written in FORTRAN 77.

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