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moment generating function

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  • Moment-generating function — In probability theory and statistics, the moment generating function of any random variable is an alternative definition of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with… …   Wikipedia

  • Factorial moment generating function — In probability theory and statistics, the factorial moment generating function of the probability distribution of a real valued random variable X is defined as:M X(t)=operatorname{E}igl [t^{X}igr] for all complex numbers t for which this… …   Wikipedia

  • Generating function — This article is about generating functions in mathematics. For generating functions in classical mechanics, see Generating function (physics). For signalling molecule, see Epidermal growth factor. In mathematics, a generating function is a formal …   Wikipedia

  • Probability-generating function — In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are… …   Wikipedia

  • Logmoment generating function — In mathematics, the logarithmic momentum generating function (equivalent to cumulant generating function) ( logmoment gen func ) is defined as follows::mu {Y}(s)=ln E(e^{scdot Y})where Y is a random variable.Thus, if Y is a discrete random… …   Wikipedia

  • Moment (mathematics) — Second moment redirects here. For the technique in probability theory, see Second moment method. See also: Moment (physics) Increasing each of the first four moments in turn while keeping the others constant, for a discrete uniform distribution… …   Wikipedia

  • Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …   Wikipedia

  • Central moment — In probability theory and statistics, central moments form one set of values by which the properties of a probability distribution can be usefully characterised. Central moments are used in preference to ordinary moments because then the values… …   Wikipedia

  • Cumulative distribution function — for the normal distributions in the image below …   Wikipedia

  • Probability density function — Boxplot and probability density function of a normal distribution N(0, σ2). In probability theory, a probability density function (pdf), or density of a continuous random variable is a function that describes the relative likelihood for this… …   Wikipedia

  • Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …   Wikipedia

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