distribution function
Noun
Meaning
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.
Examples
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.
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.
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.
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.
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.
In practice, we might not have the distribution function but the Fisher–Tippett–Gnedenko theorem provides an asymptotic result.