Hello,

we noticed that, when computing the Chi2 between a TF1 and a histogram, the Pearson and Neyman chisquares coincide. Moreover all the chisquares seem to be computed with the value of the function at the center of the bin (whereas the integral divided by the bin width should be used).

Here’s the comparison (using the function at the center of the bin):

```
Chi2(Pearson) 7.9764774712531405
Chi2(Neyman) 7.9764774712531405
Chi2(Baker-Cousins) 5.599308126733436
Chi2(Pearson) [computed from scratch] 5.470102228210528
Chi2(Neyman) [computed from scratch] 7.9764774712531405
Chi2(Baker-Cousins) [computed from scratch] 5.5993081267334395
```

We used ROOT 6.28/06 with Apple clang 15.0.0

Thanks a lot in advance,

Roberta Cardinale, Fabrizio Parodi

PS. Since new users can’t put links we add the python code and data file in the post body

------- pyROOT code -------

```
from ROOT import *
import numpy as np
h2 = TH1D("h2","",10,0,0.2)
x2 = np.loadtxt("s2.txt")
for i in range(len(x2)):
h2.Fill(x2[i])
f = TF1("exp","[0]/[1]*exp(-x/[1])",0,0.2);
f.SetParameter(0,h2.GetEntries()*h2.GetBinWidth(1))
f.SetParameter(1,0.105)
chi2N = h2.Chisquare(f,"N");
chi2P = h2.Chisquare(f,"P");
chi2BC = h2.Chisquare(f,"L");
print("Chi2(Pearson) ",chi2P)
print("Chi2(Neyman) ",chi2N)
print("Chi2(Baker-Cousins) ",chi2BC)
mchi2P=0
mchi2N=0
mchi2BC = 0
for i in range(h2.GetNbinsX()):
xmin = h2.GetBinCenter(i+1)-h2.GetBinWidth(1)/2
xmax = h2.GetBinCenter(i+1)+h2.GetBinWidth(1)/2
'''
fexp = f.Integral(xmin,xmax)/h2.GetBinWidth(1)
'''
fexp = f((xmax+xmin)/2)
N = h2.GetBinContent(i+1)
if N!=0:
mchi2N += (N-fexp)**2/N
mchi2P += (N-fexp)**2/fexp
mchi2BC += -2*(-fexp + N - N*(log(N/fexp)))
print("Chi2(Pearson) [computed from scratch] ",mchi2P)
print("Chi2(Neyman) [computed from scratch] ",mchi2N)
print("Chi2(Baker-Cousins) [computed from scratch] ",mchi2BC)
```

— data file used ----

```
2.5828444588394796e-05
0.18145581427987648
0.1263659805433976
0.005424387252062355
0.14624994234158106
0.07236607929535993
0.004345362449683603
0.0295303920904529
0.06161052939065797
0.030116863335391143
0.027451079819355365
0.041758331622220105
0.11531604906417892
0.021765487331107784
0.06545572141691491
0.17803898180619235
0.07433258746190237
0.09356927547189414
0.15065759232044093
0.15455693393438372
0.349544638577825
0.10979947298734308
0.16391301428464833
0.005792917824559513
0.054484498412083686
0.010724578301441518
0.04071205804629209
0.06959304306278759
0.05786972361949642
0.17021858273758383
0.12156219571689578
0.21420922812052653
0.27659282992034084
0.04336708133006152
0.03210065099424145
0.04507797446633408
0.033703330666773376
0.23068316649368004
0.03577223548017721
0.2227361951639177
```