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- W2018448111 abstract "Originally it had been intended to tabulate the percentage points of the P, Q and T distributions in connexion with a specific problem, now considered in ? 3. The emphasis was shifted to the statistics themselves when it was pointed out that there might be other problems in which they could be useful. In particular, Table 1, which gives percentage points for the sample mean, should have other applications. It should be useful, for instance, in testing for Poisson processes, where some of the tests reduce to testing whether N variates can be assumed to come from the uniform distribution with limits 0, 1. In a similar way, the wide class of goodness-of-fit tests of the Kolmogorov-Smirnov or Cramer-von Mises family reduce to the same problem. For the Poisson processes, at least, the sample mean will sometimes be the best test statistic against certain alternatives (see, e.g. Lewis, 1965; Cox, 1955), and even for the general goodness-of-fit problem it can be a useful statistic (see Pearson, 1963). Professor James Durbin has also pointed out an application in time series analysis, deriving from the fact that, for a series of normally distributed independent variates, the periodogram ordinates, when divided by their sum, have distributions like the successive differences between ordered independent values from the above uniform distribution. In the next section we discuss the construction of the tables. Table 1 extends tables previously given in different format by Bhate (1951), and by Eisenhart, Deming & Martin (1963); it gives some small differences from Bhate's table, for larger values of N." @default.
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- W2018448111 date "1966-06-01" @default.
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- W2018448111 title "Statistics Connected with the Uniform Distribution: Percentage Points and Application to Testing for Randomness of Directions" @default.
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- W2018448111 doi "https://doi.org/10.2307/2334070" @default.
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