In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose...

probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function....

a probability density function, then the characteristic function is the Fourier transform (with sign reversal) of the probability density function. Thus...

is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution...

}f_{X}(u){\mathcal {L}}_{X\mid Y=y}(u)\,du}}} gives the posterior probability density function for a random variable X {\displaystyle X} given the data Y =...

the area under the probability density function from negative infinity to x {\displaystyle x} . Cumulative distribution functions are also used to specify...

than that it is contained in the distribution's support. The probability density function of the continuous uniform distribution is f ( x ) = { 1 b − a...

joint probability distribution can be expressed in terms of a joint cumulative distribution function and either in terms of a joint probability density function...

current (i.e. the probability current density) is related to the probability density function via a continuity equation. The probability current is invariant...

of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population...

distribution for a real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle...

distribution is known, then the marginal probability density function can be obtained by integrating the joint probability density, f, over Y, and vice versa. That...

illustration involves a continuous probability distribution, for which the random variables have a probability density function. The second illustration, for...

and continuous probability distributions (a more general definition is discussed below). Given a probability density or mass function x ↦ f ( x ∣ θ )...

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment...

density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers...

with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions...

experiment Probability density function, a local differential probability measure for continuous random variables Probability mass function (a.k.a. discrete...

modulus of this quantity at a point in space represents a probability density at that point. Probability amplitudes provide a relationship between the quantum...

A mode of a continuous probability distribution is often considered to be any value x at which its probability density function has a locally maximum value...

probability theory, a 2-EPT probability density function is a class of probability density functions on the real line. The class contains the density...

In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of...

distribution of order K ≥ 2 with parameters α1, ..., αK > 0 has a probability density function with respect to Lebesgue measure on the Euclidean space RK−1...

physicist Eugene Wigner, is the probability distribution defined on the domain [−R, R] whose probability density function f is a scaled semicircle, i.e...

over the variance parameter. Student's t distribution has the probability density function (PDF) given by f ( t ) = Γ ( ν + 1 2 ) π ν Γ ( ν 2 ) ( 1 + t...

distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The...

In probability and statistics, the quantile function is a function Q : [ 0 , 1 ] ↦ R {\displaystyle Q:[0,1]\mapsto \mathbb {R} } which maps some probability...

point. The zeroth moment of any probability density function is 1, since the area under any probability density function must be equal to one. The normalised...

half-plane. It is one of the few stable distributions with a probability density function that can be expressed analytically, the others being the normal...

In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each...