This article discussed alternative hypotheses, including a stochastic ordering ( where the cumulative distribution functions satisfied the pointwise inequality ).
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Other approaches include the use of a decay function, such as a logarithm or placement on a cumulative distribution function.
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Note on terminology : some authors use the term " continuous distribution " to denote the distribution with continuous cumulative distribution function.
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The number " z " follows from the cumulative distribution function, in this case the cumulative normal distribution function:
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This can be avoided by using a transformation like cloglog, probit or logit ( or any inverse cumulative distribution function ).
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A number of results exist to quantify the rate of convergence of the empirical distribution function to the underlying cumulative distribution function.
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The functions f ( x ) and F ( x ) are the unconditional density and unconditional cumulative distribution function, respectively.
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Curiously, the percentile ranks for the scores between 350 and 525 seem to follow a sort of normal, cumulative distribution.
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Where is the cumulative distribution function of the standard normal distribution, and takes on the role of the inverse link function.
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Mathematicians call distributions with probability density functions "'absolutely continuous "', since their cumulative distribution function is others.
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