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Distribution Function
Distribution function may refer to *Cumulative distribution function, a basic concept of probability theory *Distribution function (physics) :''This article describes the ''distribution function'' as used in physics. You may be looking for the related mathematical concepts of cumulative distribution function or probability density function.'' In molecular kinetic theory in physics, a ..., a function giving the number of particles per unit volume in single-particle phase space * Distribution function (measure theory), a generalization of the probabilistic concept {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution Function (physics)
:''This article describes the ''distribution function'' as used in physics. You may be looking for the related mathematical concepts of cumulative distribution function or probability density function.'' In molecular kinetic theory in physics, a system's distribution function is a function of seven variables, f(x,y,z,t;v_x,v_y,v_z), which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity \mathbf=(v_x,v_y,v_z) near the position \mathbf=(x,y,z) and time t. The usual normalization of the distribution function is :n(x,y,z,t) = \int f \,dv_x \,dv_y \,dv_z, :N(t) = \int n \,dx \,dy \,dz, where, ''N'' is the total number of particles, and ''n'' is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles. A distribution function may be specialised with respect to a particular set of dimensions. E.g. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
