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...

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

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...

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

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...

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

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...

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

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

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...

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...

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...

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

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

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...

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...

"probably not fair". Posterior probability density function, or PDF (Bayesian approach). Initially, the true probability of obtaining a particular side...

variables with probability density functions f {\displaystyle f} and g {\displaystyle g} , respectively, then the probability density of the difference...