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...

}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...

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

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...

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...

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

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...

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

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...

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

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

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...

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

of zero and a variance of α2 / 4. The general formula for the probability density function (pdf) is f ( x ) = x − μ β + β x − μ 2 γ ( x − μ ) ϕ ( x − μ...

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

> 0 {\displaystyle \alpha _{1},\ldots ,\alpha _{K}>0} has a probability density function with respect to Lebesgue measure on the Euclidean space R K −...

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...

ideal gas (chi distribution with three degrees of freedom). The probability density function (pdf) of the chi-distribution is f ( x ; k ) = { x k − 1 e −...

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

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

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...

In terms of the random vector (x,y), the distribution has the probability density function (pdf) f ( x , y ; α , β ) = β − 1 π α 2 [ 1 + ( x 2 + y 2 α 2...