# Binomial Error Weighted Events

## Contents |

for exponential distribution **with a large fraction of entries** in a small number of bins. The formula. the error on sum_w is sqrt(90.1) = 9.49 . I hope to introduce a better error calculation in the case of weights in the TEfficiency class.

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## Weighted Binomial Distribution

call hfill (id,......) If you also want error bars on the plot, add "call hbarx(id)" after hidopt. These two mistakes by chance compensate to the correct final formula (poissonian and error propagation quadratic). The system returned: (22) Invalid argument The remote host or network may be down. This is the case e.g.

The usage of binomial statistics **means that you consider** the number of trials fixed to the number of entries in the given histogram. Since we are doing this, the application of the binomial statistics seems to be adequat in our case . Return to previous page . Author of this page: Ralf The number of equivalent events you get with "x=hstati(id,...)" or from PAW shell by $HINFO(id,'events'). Error Histogram In Neural Network Generated Sun, 02 Oct 2016 10:34:49 GMT by s_hv977 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection

Your relative error is 9.49/91 = 0.105. Binomial Error Bars Please try the request again. The system returned: (22) Invalid argument The remote host or network may be down. For our cos(zenit)-distribution it is about 30%.

Generated Sun, 02 Oct 2016 10:34:49 GMT by s_hv977 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.4/ Connection Histogram Error Bars Also, this effect can get big e.g. Recommended exercise for all who believed he was right, since the mistake in his ansatz is dangerous for similar cases. Please try the request again.

## Binomial Error Bars

Please try the request again. This means your statistics fluctuation is about as good (or bad) as for 92 events with event-weight==1. Weighted Binomial Distribution The system returned: (22) Invalid argument The remote host or network may be down. Binomial Standard Deviation The system returned: (22) Invalid argument The remote host or network may be down.

So, the "equivalent" statistics of MC is only about 12 times the data ! For consideration of Poissonian statistics only, here are the cos(zenit) plots, for bin=0.025, for bin=0.050, and for bin=0.10. (The latest suggestion was using Poissonian error bars for the Nature paper.) Consequences: Booking, Plotting weighted errors in PAW. limit coming out absolutely wrong: Error=0 instead of sqrt(N) ! What Is Error Histogram

The variance var(w_i) of weight w_i is determined only by the statistical fluctuation of the number of events considered, var(w_i) = var(w_i * 1 event) = w_i^2 * var(1 event) = making an (implicitely normalized) density or shape distribution. If this sounds difficult at first glance, just make the exercise and construct error propagation where you have 100 events split into two groups, with 90 events w_i==1.0 and 10 events Number of Equivalent Events.

In certain regions of variable space, or for different distribution functions of the weights (which is the relevant quantity here !! ) you can be much better or worse ! Poisson Error Bars For the example above: The number of equivalent events there is N_equ = (sum_w)^2 / var(w_i) = 91.9 events. Currently the class does not support weighted events Lorenzo Top moneta Posts: 2322 Joined: Fri Jun 03, 2005 15:38 Location: CERN Re: binomial error with weighted events Quote Unread postby moneta

## Find here the first discussion from August, 2nd,2000.

for the cos(zenit)-distribution will quantitatively change. Errors in unweighted histograms: How to correctly assign errors to unweighted events ? Please try the request again. The system returned: (22) Invalid argument The remote host or network may be down. Sumw2 Root Your cache administrator is webmaster.

If neglecting this, you get an upscaling of the errors up to 13% in the cos(zenith) plots. Derivation of the formula. Moderators: cranmer, rootdev Post Reply Search Advanced search First unread post • 3 posts • Page 1 of 1 PaulineBernat Posts: 3 Joined: Sat Dec 04, 2010 19:03 binomial error with if you compare the data to another data set, i.e.

the "error on the weighted number of events" in that bin) is given by error propagation (err(sum_w))^2 == var(sum_w) = sum {var(w_i)} (i=1,N) , i.e. Please post bug reports in Jira. We consider a bin of a histogram with N entries of weigthed events with weigths w_i, i=1,N. Your cache administrator is webmaster.

Note also, that the other MC-sample used (Eva's events) contain 2100 events (weight=1.) and have the same statistical significance. Your cache administrator is webmaster. Generated Sun, 02 Oct 2016 10:34:49 GMT by s_hv977 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection Your cache administrator is webmaster.

Errors in weighted histograms. The true statistics the distribution of N_k entries in a histogram bin with N entries in the histogram in total is following a binomial statistics. The problems: (1) His "Ansatz" neglects any statistics fluctuation of the data sample. (2) He makes a numerically wrong assumption about the second term being small. adding the squares of the errors on the weighted events.

You see that the formula given in ansatz must be wrong immediately from the weigth==1. Your cache administrator is webmaster. Your cache administrator is webmaster. Please try the request again.

Generated Sun, 02 Oct 2016 10:34:49 GMT by s_hv977 (squid/3.5.20) This is not fully correct. Original discussion of Errors and binning of the cos(zenit)-Plot for Nature. The system returned: (22) Invalid argument The remote host or network may be down.

In the division of histograms I put the "B" option to get the binomial error.I would like to know how this binomial error is calculated when the events have a weight?Thanks,Pauline The number of equivalent events is defined as N_equ = ( sum_{w_i} )^2 / sum {w_i^2} .