# Added cdf and quantiles for normal and chi-squared distribution

**URL:** <https://discuss.hail.is/t/added-cdf-and-quantiles-for-normal-and-chi-squared-distribution/88>\
**Category:** Updates\
**Created:** [November 21, 2016, 5:39pm UTC](https://discuss.hail.is/t/added-cdf-and-quantiles-for-normal-and-chi-squared-distribution/88 "2016-11-21T17:39:53Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![jbloom](https://yyz2.discourse-cdn.com/flex036/user_avatar/discuss.hail.is/jbloom/32/109_2.png) [@jbloom](https://discuss.hail.is/u/jbloom)\
**Post date:** [November 21, 2016, 5:39pm UTC](https://discuss.hail.is/t/added-cdf-and-quantiles-for-normal-and-chi-squared-distribution/88/1 "2016-11-21T17:39:54Z")

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Meta-analyses and many other workflows make use of the cumulative and inverse cumulative distribution functions for the standard normal distribution and chi-squared distribution with 1 degree of freedom. So we’ve added efficient implementations of these fundamental functions to the expression language: see the new Statistics section in the [expression language function docs](https://hail.is/docs/stable/functions.html) for details on `pnorm`, `qnorm`, `pchisq1tail` and `qchisq1tail`.

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**Author:** ![jbloom](https://yyz2.discourse-cdn.com/flex036/user_avatar/discuss.hail.is/jbloom/32/109_2.png) [@jbloom](https://discuss.hail.is/u/jbloom)\
**Post date:** [February 18, 2017, 4:30pm UTC](https://discuss.hail.is/t/added-cdf-and-quantiles-for-normal-and-chi-squared-distribution/88/2 "2017-02-18T16:30:08Z")

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The functions `pchisq1tail(x)` and `qchisq1tail(p)` have been replaced by the more general functions `pchisqtail(x,df)` and `qchisqtail(p,df)`, where `df` is the number of degrees of freedom.