# Calibration of beta inflated in brms

**URL:** <https://discourse.mc-stan.org/t/calibration-of-beta-inflated-in-brms/34745>\
**Category:** brms\
**Created:** [April 8, 2024, 8:06am UTC](https://discourse.mc-stan.org/t/calibration-of-beta-inflated-in-brms/34745 "2024-04-08T08:06:19Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![aurelien2024](https://avatars.discourse-cdn.com/v4/letter/a/ccd318/32.png) [@aurelien2024](https://discourse.mc-stan.org/u/aurelien2024)\
**Post date:** [April 8, 2024, 8:06am UTC](https://discourse.mc-stan.org/t/calibration-of-beta-inflated-in-brms/34745/1 "2024-04-08T08:06:19Z")

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Good morning. I try to understand how beta inflated [0,1[works (or [0,1]). For Poisson inflated or Gamma inflated, it is just a matter of changing the distribution in 0 but 0 is defined in the distribution ({0,1,2,3,...} for Poisson and [0,+\infty[for Gamma). But for Beta, the definition of the density is on]0,1[. So if you include zero, how does it work ? I guess there’s still the same monotonous bijection between Beta parameter space]0,+\infty[and]-\infty,+\infty[the parameter space for]0,1[ values of the explicated variable. But how is calibrated the weight in zero ?

```no-highlight
                          family = "zero_inflated_beta",
                          link = "logit",
                          link_phi = "log",
                          link_zi = "logit"
                        )

```

(so here zi = z I guess)

For zero-inflated, brms parametrization vignette says f\_Z(y)=z+(1-z)f(0) if y=0 and f\_Z(y)=(1-z)f(y) if y\>0. For Hurdle family f\_Z(y)=z if y=0 and f\_Z(y)=(1-z)f(y)/(1-f(0)) if y\>0.

I guess the question also apply for zero-one beta inflated.

Thank you!

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<div class="post-metadata">

**Author:** ![aurelien2024](https://avatars.discourse-cdn.com/v4/letter/a/ccd318/32.png) [@aurelien2024](https://discourse.mc-stan.org/u/aurelien2024)\
**Post date:** [April 8, 2024, 8:45am UTC](https://discourse.mc-stan.org/t/calibration-of-beta-inflated-in-brms/34745/2 "2024-04-08T08:45:25Z")

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And sorry, but f(0) is not defined for beta distribution… So ?