# cumulative distribution function

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## cumulative distribution function

n
(Statistics) statistics a function defined on the sample space of a distribution and taking as its value at each point the probability that the random variable has that value or less. The function F(x) = P(Xx) where X is the random variable, which is the sum or integral of the probability density function of the distribution. Sometimes shortened to: distribution function
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Similarly, to describe their joint distribution, we can use corresponding 2D cumulative distribution function (cdf)
The cumulative distribution function for the normal distribution is given as follows:
Let us now show the relationship between this function and other standard special functions (integral of error function) [4] as error function and cumulative distribution function for normal distribution in the context of its use.
The cumulative distribution function, moment, and stochastic representation will be presented when they correspond to the cases at hand.
For the analysis of the degree distribution, a common approach is to plot the complementary cumulative distribution function P(k), which represents the fraction of nodes with degrees greater than or equal to k in the entire network.
The cumulative distribution function of nonparametric probabilities of non-correlation with sex (Figure 4a) shows a very strong profile, affecting more than 30% of the peaks.
In addition to achieving the primary endpoint (response rate) of non-inferiority versus treatment with daily sublingual buprenorphine/naloxone, the current standard of care, CAM2038 also demonstrated superior treatment effect for the secondary endpoint (Cumulative Distribution Function of the percentage of urine toxicology negative for illicit opioids confirmed by self-report).
We reject [H.sub.0] if |z|>[z.sub.[alpha]/2], where [z.sub.[alpha]/2] denotes the upper [alpha]/2 quantile of the standard normal distribution, i.e., [PHI]([z.sub.[alpha]/2]) = 1- [alpha]/2, with [PHI] denoting the cumulative distribution function of the standard normal distribution.
In order to test if the Pareto power law distribution fits the data well, the complementary cumulative distribution function (C-CDF), Eq.
Probability distribution value can be calculated using cumulative distribution function (CDF) and probability density function (PDF) of the captured image, whose values are achieved by brightness distribution of the captured image.
It also includes sophisticated software features, such as the complementary cumulative distribution function (CCDF), automatic current, and power profiling.

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