Maxwell distribution

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See also: Chi Squared distribution

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Format: VoseMaxwell(a, U)

Maxwell equations

The Maxwell, or Maxwell–Boltzmann, distribution describes particle speeds in gases, where the particles do not constantly interact with each other but move freely between short collisions. It describes the probability distribution of a particle's speed.

 

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Uses

The Maxwell–Boltzmann distribution applies to ideal gases close to thermodynamic equilibrium. It forms the basis of the kinetic theory of gases, which explains many fundamental gas properties, including pressure and diffusion.

Comments

The a parameter only changes the scale. The distribution always has the same shape.

Named after James Clerk Maxwell and Ludwig Boltzmann.

The distribution is the magnitude of a 3-dimensional vector whose components are independent and normally distributed with mean 0 and standard deviation a :


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Thus, the Maxwell and Chi Squared distributions are related as follows:

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VoseFunctions for this distribution

VoseMaxwell generates values from this distribution or calculates a percentile. Professional and Industrial editions only.

VoseMaxwellObject constructs a distribution object for this distribution. Professional and Industrial editions only.

VoseMaxwellProb returns the probability density or cumulative distribution function for this distribution. Professional and Industrial editions only.

VoseMaxwellProb10 returns the log10 of the probability density or cumulative distribution function. Professional and Industrial editions only.

VoseMaxwellFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution. Professional and Industrial editions only.

VoseMaxwellFitObject constructs a distribution object of this distribution fitted to data. Professional and Industrial editions only.

VoseMaxwellFitP returns the parameters of this distribution fitted to data. Professional and Industrial editions only.