Normalize edisp to integral of 1, not sum of 1

[maxnoe]

@RuneDominik does this have also implications on the interpolation code?

[codecov[bot]]

Codecov Report

Patch coverage: 99.35% and project coverage change: +0.05% :tada:

Comparison is base (19fff68) 94.73% compared to head (1164644) 94.78%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #250 +/- ## ========================================== + Coverage 94.73% 94.78% +0.05% ========================================== Files 60 60 Lines 2981 3050 +69 ========================================== + Hits 2824 2891 +67 - Misses 157 159 +2 ``` | [Files Changed](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory) | Coverage Δ | | |---|---|---| | [pyirf/interpolation/\_\_init\_\_.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9fX2luaXRfXy5weQ==) | `100.00% <ø> (ø)` | | | [pyirf/interpolation/utils.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi91dGlscy5weQ==) | `97.61% <88.88%> (-2.39%)` | :arrow_down: | | [pyirf/interpolation/component\_estimators.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9jb21wb25lbnRfZXN0aW1hdG9ycy5weQ==) | `99.27% <92.85%> (-0.73%)` | :arrow_down: | | [pyirf/interpolation/base\_extrapolators.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9iYXNlX2V4dHJhcG9sYXRvcnMucHk=) | `100.00% <100.00%> (ø)` | | | [pyirf/interpolation/base\_interpolators.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9iYXNlX2ludGVycG9sYXRvcnMucHk=) | `96.87% <100.00%> (+0.57%)` | :arrow_up: | | [pyirf/interpolation/moment\_morph\_interpolator.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9tb21lbnRfbW9ycGhfaW50ZXJwb2xhdG9yLnB5) | `100.00% <100.00%> (ø)` | | | [pyirf/interpolation/nearest\_neighbor\_searcher.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9uZWFyZXN0X25laWdoYm9yX3NlYXJjaGVyLnB5) | `100.00% <100.00%> (ø)` | | | [...yirf/interpolation/nearest\_simplex\_extrapolator.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9uZWFyZXN0X3NpbXBsZXhfZXh0cmFwb2xhdG9yLnB5) | `100.00% <100.00%> (ø)` | | | [pyirf/interpolation/quantile\_interpolator.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi9xdWFudGlsZV9pbnRlcnBvbGF0b3IucHk=) | `98.24% <100.00%> (+0.09%)` | :arrow_up: | | [...irf/interpolation/tests/test\_base\_extrapolators.py](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory#diff-cHlpcmYvaW50ZXJwb2xhdGlvbi90ZXN0cy90ZXN0X2Jhc2VfZXh0cmFwb2xhdG9ycy5weQ==) | `100.00% <100.00%> (ø)` | | | ... and [10 more](https://app.codecov.io/gh/cta-observatory/pyirf/pull/250?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=cta-observatory) | |

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[RuneDominik]

Yes, it does. At the moment MomentMoprhInterpolator, QuantileInterpolator and MomentMorphNearestSimplexExtrapolator also norm to a sum of one. As this however only is a global factor, we could just nomalize by integration in EnergyDispersionEstimator after computing the interpolant, right?

Edit: There are probably more things that need to be changed. E.g. adding some factors to mean_std_estimation

I'm however not sure how this effects the performance of the algorithms. All EDisps I've used so far for testing summed to one as they were computed with pyirf.

[maxnoe]

@RuneDominik done