# DistributionParameterAssumptions

gives a logical expression for assumptions on parameters in the symbolic distribution dist.

# Examples

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## Basic Examples(1)

Obtain parameter assumptions for a normal distribution:

Parameter assumptions for a multinomial distribution:

## Scope(4)

Obtain assumptions for distributions with combinations of numeric and symbolic parameters:

Get assumptions for univariate and multivariate discrete and continuous distributions:

Get assumptions for a derived distribution:

Data distributions have no parameters, so the assumptions are vacuously true:

## Applications(4)

Get the PDF for an extreme value distribution:

Compute the integral for its mean without including parameter assumptions:

Use parameter assumptions to simplify the result:

Compute the result by giving the assumptions directly to Integrate:

Compare with the mean of the distribution:

Define two χ2 distributions and their parameter assumptions:

Compute the pdf of the sum of the χ2 distributed variables via convolution with assumptions:

Verify the additive property of χ2 variables:

Define a Haight distribution with probability parameter :

Sum the PDF expression to check normalization:

The result is not always unity if the distribution assumptions are not met:

Give assumptions to Sum to verify the total probability is 1 for assumed values of :

Get the assumptions for a type 1 Pearson with unknown b1 and b0 parameters:

Find the maximum possible value of b1 as a function of b0:

## Properties & Relations(1)

DistributionParameterAssumptions returns conditions on parameters:

DistributionParameterQ assumes symbolic parameters are valid:

With numeric parameters, the outputs are equivalent:

Wolfram Research (2010), DistributionParameterAssumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html.

#### Text

Wolfram Research (2010), DistributionParameterAssumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html.

#### CMS

Wolfram Language. 2010. "DistributionParameterAssumptions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html.

#### APA

Wolfram Language. (2010). DistributionParameterAssumptions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html

#### BibTeX

@misc{reference.wolfram_2022_distributionparameterassumptions, author="Wolfram Research", title="{DistributionParameterAssumptions}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html}", note=[Accessed: 23-March-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_distributionparameterassumptions, organization={Wolfram Research}, title={DistributionParameterAssumptions}, year={2010}, url={https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html}, note=[Accessed: 23-March-2023 ]}