Noun
distribution function (plural distribution functions)
(mathematics, physics) A function of seven variables of the form
f
(
x
,
y
,
z
,
t
;
v
x
,
v
y
,
v
z
)
{\displaystyle f(x,y,z,t;v_{x},v_{y},v_{z})}
that gives the number of particles per unit volume in single-particle phase space.
Alternatively, for a cumulative distribution function F(x) with inverse x(F), the Lorenz curve L(F) is directly given by: : The inverse x(F) may not exist because the cumulative distribution function has intervals of constant values. Source: Internet
Each realization is a sample of the complete N -dimensional joint distribution function :: : In this approach, the presence of multiple solutions to the interpolation problem is acknowledged. Source: Internet
In practice, a bidirectional reflectance distribution function (BRDF) may be required to accurately characterize the scattering properties of a surface, but albedo is very useful as a first approximation. Source: Internet
Examples * As an example, suppose we have a random variable and a cumulative distribution function : In order to perform an inversion we want to solve for : : From here we would perform steps one, two and three. Source: Internet
Furthermore, : Every function with these four properties is a CDF, i.e., for every such function, a random variable can be defined such that the function is the cumulative distribution function of that random variable. Source: Internet
In practice, we might not have the distribution function but the Fisher–Tippett–Gnedenko theorem provides an asymptotic result. Source: Internet