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DirichletDistribution

DirichletDistribution
represents a Dirichlet distribution of dimension k with shape parameters .
  • The probability density for vector in a Dirichlet distribution is proportional to for and .
Probability density function in two dimensions:
Cumulative distribution function in two dimensions:
Mean and variance in two dimensions:
Covariance:
Probability density function in two dimensions:
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Cumulative distribution function in two dimensions:
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Mean and variance in two dimensions:
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Covariance:
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Generate a set of pseudorandom vectors that follow a bivariate Dirichlet distribution:
Visualize the sample using a histogram:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Goodness-of-fit test:
Skewness:
Kurtosis:
Correlation:
Different mixed moments for a Dirichlet distribution:
Closed form for a symbolic order:
Mixed central moments:
Mixed factorial moments:
Mixed cumulants:
Hazard function:
Univariate marginals of a Dirichlet distribution follow a BetaDistribution:
Multivariate marginals follow a DirichletDistribution:
Show a distribution function and its histogram in the same plot:
Compare the PDF to its histogram version:
Compare the CDF to its histogram version:
Simulate points on the half-plane with mean :
For :
For :
The point spread can be controlled by the third parameter:
Use Dirichlet distribution to define a multivariate Polya distribution as a parameter mixture:
Probability density function:
Equal probability contours for a binormal distribution:
One dimensional Dirichlet distribution is a BetaDistribution:
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