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This article describes the distribution function as used in physics.

Let be the empirical distribution function based on the sample.

The distribution function depends on the three-dimensional position, the energy and magnetic moment.

However, in general the cumulative distribution function does not have a closed form solution.

This follows from the form of the cumulative distribution function given above.

"The state of having identical cumulative distribution function or values".

The distribution function is a property of the experimental pattern.

Running the experimental pattern results in a measurement of the distribution function.

The distribution function does not bring any knowledge nor information about "what happens inside the experimental device".

The distribution function is constant along any trajectory in phase space.

Its cumulative distribution function is sometimes referred to as the Devil's staircase, although that term has a more general meaning.

It can also be used to refer to the empirical cumulative distribution function.

In statistical software R, the cumulative distribution function is implemented as pt.

A third form of the density is obtained using its cumulative distribution functions, as follows.

However, in general the cumulative distribution function does not have a closed form solution.

This follows from the form of the cumulative distribution function given above.

"The state of having identical cumulative distribution function or values".

Its cumulative distribution function can be written in closed form, unlike that of the log-normal.

The latter can be seen by calculating the cumulative distribution function for s in the interval (0, 1).

Here, is the cumulative distribution function of the student distribution.