represents a mixture distribution whose CDF is given as a sum of the CDFs of the component distributions disti, each with weight wi.
- The cumulative distribution function for value is proportional to , where is the CDF for disti.
- The distributions disti need to be all continuous or all discrete, and have the same dimensionality.
- The weights wi can be any non-negative real numbers.
- MixtureDistribution can be used with such functions as Mean, CDF, and RandomVariate, etc.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (10)
Parametric Distributions (5)
Nonparametric Distributions (3)
Define a mixture with SmoothKernelDistribution:
Define a mixture with EmpiricalDistribution:
Define a mixture with HistogramDistribution:
Derived Distributions (10)
Define a mixture distribution with components given by MixtureDistribution:
Find a mixture distribution of the OrderDistribution of the minimum and the maximum:
Find the mixture distribution of a TruncatedDistribution:
Find the probability density function of the mixture distribution with a ProductDistribution:
Define a mixture distribution with a TransformedDistribution:
Define a mixture distribution of a MarginalDistribution:
Define a mixture with a CensoredDistribution:
A mixture with a ParameterMixtureDistribution:
Define a mixture distribution with a CopulaDistribution:
Plot the PDF:
Package it up as a function using NProbability:
The heights of females in the United States follow normal distribution with mean 64 inches and standard deviation of 2 inches, while the heights of males in the United States follow normal distribution with mean 70 inches and standard deviation of 2 inches. If the population ratio of males to females is 1.1, then the heights of the whole population have the following bimodal distribution:
MixtureDistribution can be used to create multimodal models:
Assuming 65% of the driving is done in the city, the mileage follows a MixtureDistribution:
Visualize the distribution of pixel values via Histogram:
Fit the pixel values to a three-component Gaussian mixture with EstimatedDistribution:
Properties & Relations (8)
A mixture with weights w is equivalent to one with weights w/Total[w]:
A ParameterMixtureDistribution with a discrete weight, assuming a finite number of values, can be represented as a mixture distribution:
A ParameterMixtureDistribution with a discrete weight, assuming a countable number of values, can be approximated by a mixture distribution:
Approximating a ParameterMixtureDistribution with a continuous weight by a mixture distribution:
Wolfram Research (2010), MixtureDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/MixtureDistribution.html (updated 2016).
Wolfram Language. 2010. "MixtureDistribution." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/MixtureDistribution.html.
Wolfram Language. (2010). MixtureDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MixtureDistribution.html