MaxwellDistribution

Generate a set of random numbers that are Maxwell distributed:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness and kurtosis are constant:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

Consider vectors with standard normal components:

The angle in spherical coordinates follows a uniform distribution:

The norm will follow a Maxwell distribution:

Velocity density function along any direction of a gas molecule follows normal distribution with mean 0 and standard deviation . The distribution of the speeds of molecules in a hydrogen gas at 573 K is given:

Find the probability that a hydrogen molecule has speed at least :

Find the average speed of such a molecule:

Simulate the speed of 100 hydrogen molecules in the above conditions:

Parameter influence on the CDF for each :

Maxwell distribution is closed under scaling by a positive factor:

The variance is proportional to the square of the mean:

Relationships to other distributions:

MaxwellDistribution with is a special case of ChiDistribution:

Square of MaxwellDistribution with is a special case of ChiSquareDistribution:

MaxwellDistribution is a special case of GammaDistribution:

The norm of three standard normally distributed variables follows Maxwell distribution:

MaxwellDistribution is not defined when is not a positive real number:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:

Consider vectors with standard normal components:

The regions between the spheres each have a tenth of the vectors in them: