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The Wald–Wolfowitz runs test (or simply runs test), named after statisticians Abraham Wald and Jacob Wolfowitz is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data sequence. More precisely, it can be used to test the hypothesis that the elements of the sequence are mutually independent.
The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald [1] and later proven to be optimal by Wald and Jacob Wolfowitz. [2] Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem.
A randomness test (or test for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see whether it can be described as random (patternless). In stochastic modeling , as in some computer simulations , the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to ...
The Wald–Wolfowitz runs test tests for the number of bit transitions between 0 bits, and 1 bits, comparing the observed frequencies with expected frequency of a random bit sequence. Information entropy; Autocorrelation test; Kolmogorov–Smirnov test; Statistically distance based randomness test.
There are several reasons to prefer the likelihood ratio test or the Lagrange multiplier to the Wald test: [18] [19] [20] Non-invariance: As argued above, the Wald test is not invariant under reparametrization, while the likelihood ratio tests will give exactly the same answer whether we work with R, log R or any other monotonic transformation ...
Abraham Wald (/ w ɔː l d /; Hungarian: Wald Ábrahám, Yiddish: אברהם וואַלד; () 31 October 1902 – () 13 December 1950) was a Jewish Hungarian mathematician who contributed to decision theory, [1] geometry and econometrics, and founded the field of sequential analysis. [2]
There are several methods of finding an optimal design, given an a priori restriction on the number of experimental runs or replications. Some of these methods are discussed by Atkinson, Donev and Tobias and in the paper by Hardin and Sloane. Of course, fixing the number of experimental runs a priori would be impractical. Prudent statisticians ...
The inverse Gaussian distribution is a two-parameter exponential family with natural parameters −λ/(2μ 2) and −λ/2, and natural statistics X and 1/X.. For > fixed, it is also a single-parameter natural exponential family distribution [4] where the base distribution has density