# Which Distribution for Constrained Parameter vector Sum

**URL:** https://discourse.pymc.io/t/which-distribution-for-constrained-parameter-vector-sum/1692
**Category:** Questions
**Created:** [August 9, 2018, 9:20pm UTC](https://discourse.pymc.io/t/which-distribution-for-constrained-parameter-vector-sum/1692 "2018-08-09T21:20:12Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![ded](https://avatars.discourse-cdn.com/v4/letter/d/278dde/32.png) [@ded](https://discourse.pymc.io/u/ded)
#### Post date: [August 9, 2018, 9:20pm UTC](https://discourse.pymc.io/t/which-distribution-for-constrained-parameter-vector-sum/1692/1 "2018-08-09T21:20:12Z")

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Hi.

I would like to have a vector of K parameters [B1… BK].  
The main constraint I have is that their sum is 1.  
No particular distribution is needed, except, I would like that the first parameter (B1) be larger than the rest. I can set it to some value.

How should I declare my B param vector?

Thanks in advance

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### Author: ![ded](https://avatars.discourse-cdn.com/v4/letter/d/278dde/32.png) [@ded](https://discourse.pymc.io/u/ded)
#### Post date: [August 10, 2018, 1:23am UTC](https://discourse.pymc.io/t/which-distribution-for-constrained-parameter-vector-sum/1692/2 "2018-08-10T01:23:02Z")

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I think I am solving this for now with:  
B = pm.Dirichlet(‘proportions’, np.ones(K))  
Though, I don’t know yet how to pin the first parameter B[0] to be sufficiently large (~ 0.5)  
any idea?

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### Author: ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)
#### Post date: [August 10, 2018, 4:33am UTC](https://discourse.pymc.io/t/which-distribution-for-constrained-parameter-vector-sum/1692/3 "2018-08-10T04:33:18Z")

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You can control that by playing with the prior parameter of Dirichlet [https://en.wikipedia.org/wiki/Dirichlet\_distribution](https://en.wikipedia.org/wiki/Dirichlet_distribution)
