Home > Error Bars > Binomial Error Weighted Events# Binomial Error Weighted Events

## Weighted Binomial Distribution

## Binomial Error Bars

## We have sum_w = 90*1 + 10*0.1 = 91 events, the statistical fluctuation is coming from sqrt(90) and sqrt(10), giving var(w_i) = 1^2 * 90 + 0.1^2 * 10 = 90.1

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Your **cache administrator is webmaster.** Please try the request again. I hope to introduce a better error calculation in the case of weights in the TEfficiency class. limit coming out absolutely wrong: Error=0 instead of sqrt(N) !

This number relates the sample **of N weighted events to N_equ** events with w==1 that would have the same relative statistical fluctuation. 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 The system returned: (22) Invalid argument The remote host or network may be down. 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.

The system returned: (22) Invalid argument The remote host or network may be down. Your cache administrator is webmaster. Generated Sun, 02 Oct 2016 10:34:49 GMT by s_hv977 (squid/3.5.20) For our cos(zenit)-distribution it is about 30%.

Your cache administrator is webmaster. Recommended exercise for all who believed he was right, since the mistake in his ansatz is dangerous for similar cases. call hfill (id,......) If you also want error bars on the plot, add "call hbarx(id)" after hidopt. Error Histogram In Neural Network Your **cache administrator is** webmaster.

the error on sum_w is sqrt(90.1) = 9.49 . This means your statistics fluctuation is about as good (or bad) as for 92 events with event-weight==1. The system returned: (22) Invalid argument The remote host or network may be down. Derivation of the formula.

Booking, Plotting weighted errors in PAW. Histogram Error Bars The normal approximation is the same used in TH1::DivideThe TEfficiency class will be improved later since it requires some changes in the interface Cheers Lorenzo Top Display posts from previous: All The number of equivalent events is defined as N_equ = ( sum_{w_i} )^2 / sum {w_i^2} . Please try the request again.

If neglecting this, you get an upscaling of the errors up to 13% in the cos(zenith) plots. Your relative error is 9.49/91 = 0.105. Weighted Binomial Distribution Derivation of above formula is based on error propagation and intrinsic poissonian statistics only. Binomial Standard Deviation This is not fully correct.

The system returned: (22) Invalid argument The remote host or network may be down. Find here the first discussion from August, 2nd,2000. For the example above: The number of equivalent events there is N_equ = (sum_w)^2 / var(w_i) = 91.9 events. Please try the request again. What Is Error Histogram

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://0.0.0.9/ Connection Find here also the cos(zenit) plots, for bin=0.025, for bin=0.050, and for bin=0.10, recently updated for the binomial error bars for the data. The system returned: (22) Invalid argument The remote host or network may be down. For the MC-files for the atm-nu's in the Nature paper: For 7000 events we get N_equ=2200, while the number of events in the data sample is 188.

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 Poisson Error Bars See here for Gary's wrong way to derive the correct formula. Please try the request again.

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 The system returned: (22) Invalid argument The remote host or network may be down. The usage of binomial statistics means that you consider the number of trials fixed to the number of entries in the given histogram. Sumw2 Root The error of N_k comes out to err(N_k) = sqrt (N_k * (1 - N_k/N) ).

The error on sum_w is then given as err(sum_w) = sqrt( sum {w_i^2} ). We consider a bin of a histogram with N entries of weigthed events with weigths w_i, i=1,N. if you compare the data to another data set, i.e. Only a single command in Hbook or PAW (also from shell!!) is needed to get weighted error handling 'correctly' (sorry to all who knew this...) - Invoke statistics BEFORE filling the

Your cache administrator is webmaster. Please post bug reports in Jira. The number of equivalent events you get with "x=hstati(id,...)" or from PAW shell by $HINFO(id,'events'). Please try the request again.

making an (implicitely normalized) density or shape distribution. 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 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://0.0.0.8/ Connection

An erroneous way of statistics reasoning. for exponential distribution with a large fraction of entries in a small number of bins. This is the case e.g. 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 !

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