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based on an earlier version of the Wolfram Language.
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# MaxwellDistribution

 MaxwellDistribution[] represents a Maxwell distribution with scale parameter .
• The probability density for value in a Maxwell distribution is proportional to for , and is zero for . »
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (6)
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:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
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:
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: