# Quality of student parameter estimation

**URL:** <https://openturns.discourse.group/t/quality-of-student-parameter-estimation/214>\
**Category:** Python usage\
**Created:** [June 20, 2022, 9:51am UTC](https://openturns.discourse.group/t/quality-of-student-parameter-estimation/214 "2022-06-20T09:51:02Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![AlainK](https://avatars.discourse-cdn.com/v4/letter/a/58956e/32.png) [@AlainK](https://openturns.discourse.group/u/AlainK)\
**Post date:** [June 20, 2022, 9:51am UTC](https://openturns.discourse.group/t/quality-of-student-parameter-estimation/214/1 "2022-06-20T09:51:02Z")

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Dear developers,

I was trying to improve my estimation of a Student distribution from the scipy.stats method but found out that my use of OpenTURNS was way worse. So worse that I fear I made an huge mistake in using OpenTURNS.  
But the Scipy estimator gave the right answer on a sample Student distribution generated by OpenTURNS.  
Thus I am perplexed …  
Any ideas ?

Thanks

Here is my code :

```python
import openturns as ot
from scipy import stats

Nbre_mesures = 327680
ecart_type = 1
df = 1.5

# test openturns
# sample generation from scipy and parameter estimation 
# from scipy and openturns
student = stats.t.rvs(df, scale=ecart_type, size=Nbre_mesures)

sample = ot.Sample.BuildFromPoint(student)
distribution = ot.StudentFactory().build(sample)
print(stats.t.fit(student), distribution.getParameter())

# In reverse
sample = ot.Student(df, 0.0, ecart_type).getSample(Nbre_mesures)
distribution = ot.StudentFactory().buildAsStudent(sample)
print(stats.t.fit(sample), distribution.getParameter())

```

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<div class="post-metadata">

**Author:** ![AlainK](https://avatars.discourse-cdn.com/v4/letter/a/58956e/32.png) [@AlainK](https://openturns.discourse.group/u/AlainK)\
**Post date:** [June 21, 2022, 11:52am UTC](https://openturns.discourse.group/t/quality-of-student-parameter-estimation/214/2 "2022-06-21T11:52:47Z")

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and I got :

```python
WRN - TNC went to an abnormal point=[nan]

WRN - Warning! As nu <= 2, the covariance of the distribution will not be defined
(1.5033992737466937, 0.0016595840358914786, 0.9979708660554066) [2.00211,-0.0396894,1.11723]
(1.4966359121213684, -0.0023588844106721698, 0.9989014331961306) [2.01209,-0.00297962,1.12155]

```

Very bad estimation of the degree of freedom

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**Author:** ![regislebrun](https://yyz2.discourse-cdn.com/free1/user_avatar/openturns.discourse.group/regislebrun/32/154_2.png) [@regislebrun](https://openturns.discourse.group/u/regislebrun)\
**Post date:** [June 22, 2022, 5:28am UTC](https://openturns.discourse.group/t/quality-of-student-parameter-estimation/214/3 "2022-06-22T05:28:11Z")

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Hi,

Unfortunately the `StudentFactory` class does not work well for the heaviest tails, it means for \nu \leq 2 here, as it depends on the existence of the variance in a (slightly) obfuscated way. If you replace `df=1.5` by `df=2.5` you get the correct result, but even if df=2.05 is greater than 2, the results start to be strange. You may have better success using the `MaximumLikelihoodFactory` class but you will have to set the optimization bounds manually, which is not very satisfactory.  
Would you be kind enough to open an issue on Github?

Cheers

Régis