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

- DistributionParameterAssumptions returns a logical combination of equalities, inequalities, and domain specifications for assumptions on parameters in dist.
- DistributionParameterAssumptions can generate parameter assumptions for any univariate or multivariate distribution specified as a symbolic distribution.
Examples
open allclose allBasic Examples (1)Summary of the most common use cases
Scope (4)Survey of the scope of standard use cases
Obtain assumptions for distributions with combinations of numeric and symbolic parameters:

https://wolfram.com/xid/0g34083nrp1l2msnn-gx7796


https://wolfram.com/xid/0g34083nrp1l2msnn-bqe37g

Get assumptions for univariate and multivariate discrete and continuous distributions:

https://wolfram.com/xid/0g34083nrp1l2msnn-bhk6xb

https://wolfram.com/xid/0g34083nrp1l2msnn-ky735k

Get assumptions for a derived distribution:

https://wolfram.com/xid/0g34083nrp1l2msnn-3xz7c

https://wolfram.com/xid/0g34083nrp1l2msnn-fm8qpd

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

https://wolfram.com/xid/0g34083nrp1l2msnn-fb6a6o

https://wolfram.com/xid/0g34083nrp1l2msnn-c1aazc

Applications (4)Sample problems that can be solved with this function
Get the PDF for an extreme value distribution:

https://wolfram.com/xid/0g34083nrp1l2msnn-imswzt

Compute the integral for its mean without including parameter assumptions:

https://wolfram.com/xid/0g34083nrp1l2msnn-cizgeu

Use parameter assumptions to simplify the result:

https://wolfram.com/xid/0g34083nrp1l2msnn-b0qe0h

Compute the result by giving the assumptions directly to Integrate:

https://wolfram.com/xid/0g34083nrp1l2msnn-bte9fo

Compare with the mean of the distribution:

https://wolfram.com/xid/0g34083nrp1l2msnn-kepveb

Define two χ2 distributions and their parameter assumptions:

https://wolfram.com/xid/0g34083nrp1l2msnn-dfeikd
Compute the pdf of the sum of the χ2 distributed variables via convolution with assumptions:

https://wolfram.com/xid/0g34083nrp1l2msnn-89v44

Verify the additive property of χ2 variables:

https://wolfram.com/xid/0g34083nrp1l2msnn-q0r0s

Define a Haight distribution with probability parameter :

https://wolfram.com/xid/0g34083nrp1l2msnn-fp2rq
Sum the PDF expression to check normalization:

https://wolfram.com/xid/0g34083nrp1l2msnn-nwoec

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

https://wolfram.com/xid/0g34083nrp1l2msnn-la0u9t

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

https://wolfram.com/xid/0g34083nrp1l2msnn-dqcavc

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

https://wolfram.com/xid/0g34083nrp1l2msnn-c2hd18

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

https://wolfram.com/xid/0g34083nrp1l2msnn-em9qx


https://wolfram.com/xid/0g34083nrp1l2msnn-b5ahe4

Properties & Relations (1)Properties of the function, and connections to other functions
DistributionParameterAssumptions returns conditions on parameters:

https://wolfram.com/xid/0g34083nrp1l2msnn-ykgnh

DistributionParameterQ assumes symbolic parameters are valid:

https://wolfram.com/xid/0g34083nrp1l2msnn-eo9cs1

With numeric parameters, the outputs are equivalent:

https://wolfram.com/xid/0g34083nrp1l2msnn-cty9cl


https://wolfram.com/xid/0g34083nrp1l2msnn-drh8c8

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.
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.
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
Wolfram Language. (2010). DistributionParameterAssumptions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html
BibTeX
@misc{reference.wolfram_2025_distributionparameterassumptions, author="Wolfram Research", title="{DistributionParameterAssumptions}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html}", note=[Accessed: 02-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_distributionparameterassumptions, organization={Wolfram Research}, title={DistributionParameterAssumptions}, year={2010}, url={https://reference.wolfram.com/language/ref/DistributionParameterAssumptions.html}, note=[Accessed: 02-May-2025
]}