In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) satisfying and .
In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to . Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
The cumulative distribution function of a real-valued random variable is the function given by
where the right-hand side represents the probability that the random variable takes on a value less than or equal to .
The probability that lies in the semi-closed interval , where , is therefore
In the definition above, the "less than or equal to" sign, "≤", is a convention, not a universally used one (e.g. Hungarian literature uses "
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Le cours est une introduction à la théorie des probabilités. Le but sera d'introduire le formalisme moderne (basé sur la notion de mesure) et de lier celui-ci à l'aspect "intuitif" des probabilités.
This course is an introduction to quantitative risk management that covers standard statistical methods, multivariate risk factor models, non-linear dependence structures (copula models), as well as p
Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.
Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.
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Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by Frei et al. [J. Plasma Phys. 86, 905860205 (2020)], where the full-F distr ...