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The Computation of the Cumulative Distribution Function of the Erlang Distribution
Journal of Information and Optimization Sciences, 1992Two algorithms are compared for evaluating the cdf of the Erlang distribution. The first algorithm gives correct results only for some values of the parameters while the second, an approximation of...
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Permutation inversions and multidimensional cumulative distribution functions
Information Processing Letters, 1982Abstract The problem of computing the empirical cumulative distribution function (ECDF) of N points in k-dimensional space has been studied and motivated recently by Bentley [1], whose solution uses recursive multidimensional divide-and-conquer. In this paper, the problem is treated as a generalization of the problem of computing the inversion of a ...
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The Cumulative Distribution Function for a finite data set
2012 20th Signal Processing and Communications Applications Conference (SIU), 2012In this work, the Cumulative Distribution Function (CDF) and the Probability Density Function (PDF) are examined for a data set of finite elements. The CDF and the PDF are valid only for the theoretical asymptotes when the number of elements in the set approaches infinity. The equivalent functions defined for a finite set are currently unknown.
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An inequality of Ostrowski's type for cumulative distribution functions
1998The main result of the paper is the following Ostrowski type inequality. Let \(X\) be a random variable taking values in the finite interval \([a,b]\), with expectation \(E(X)\). Then we have the inequality \[ \biggl |\Pr (X\leq x)-\frac{b-E(X)}{b-a}\biggr|\leq \frac{1}{2}+\frac{|x-\frac{a+b}{2}|}{b-a} \] for all \(x\in [a,b]\).
Barnett, Neil S, Dragomir, Sever S
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Continuous Density and Cumulative Distribution Functions
2019Although we often hear that data speak for themselves, their voices can be soft and sly. Frederick Mosteller (Beginning Statistics with Data Analysis, 1983) The previous chapter emphasizes the elastic constitutive paradigm applicable to transient, recoverable deformation processes, which are accompanied by sufficiently small strain so that the ...
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