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Malamala

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In summary: Now, as this functions measure counts, the error associated to it can be considered a Poisson error i.e. assuming that I wouldn't have that error of 2, I would give my result as ##100 \pm \sqrt{10} = 100 \pm 10##. However, if the prediction is not an integer number of counts, then the error needs to be taken into account. For example, if the prediction is ##y(x) = 100 + 10## then the error is ##10 \pm \sqrt{100+10} = 10 \pm 0.1##. So, if the prediction is not an integer number of counts, then the error

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Malamala

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BvU

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With numbers like that you can ignore the error in the fitted parameters: you shouldn't quote 100 ##\pm## 10.2 because your estimate has no decimals ##\rightarrow## your error estimate doesn't either.

If the fit is a lot less accurate, say with an error of 10, then yes, I would add in quadrature if I only had to report ##y(x_0)##.

If I had to erport a series of ##y(x_i)##, I would keep the fit error separated (it's a systematic error).

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Malamala

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Thank you! So ideally I should quote my result (for a fit error of 10) as ##100 \pm (10)_{stat} \pm (10)_{sys}##. Is this right? One more question about my initial example. Assuming that using the parameters obtained by that fit i.e. ##y(x)##, I try to fit to some other data and I see a bump in a given bin, and I want to see how statistically significant it is. So in order to do that I would calculate ##|y_{bump} - y(x_{bump})|/\sigma_y##. Should I use in this case ##10.2## as the value for ##\sigma_y##? Or can I still safely use just 10?BvU said:

With numbers like that you can ignore the error in the fitted parameters: you shouldn't quote 100 ##\pm## 10.2 because your estimate has no decimals ##\rightarrow## your error estimate doesn't either.

If the fit is a lot less accurate, say with an error of 10, then yes, I would add in quadrature if I only had to report ##y(x_0)##.

If I had to erport a series of ##y(x_i)##, I would keep the fit error separated (it's a systematic error).

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BvU

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With your fit you calculate ##y(x_\text{bump}) = 100\pm 10_\text{sys}## but your measurement give you ##y_\text{bump}\pm\sqrt{y_\text{bump}}## and therefore the net height of the bump has error ##\sqrt{100 + y_\text{bump}}## .

In other words: I would ignore the statistical error in ##y(x_0)## ... (*)

This goes to show you really want a low background, and if that's done, you also want a very good fit of that background !(*) don't feel 100 (##\pm##10 % ) certain here, could use some help from e.g. @mfb

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mfb

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Stephen Tashi

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Malamala said:Hello! I have a fit to a histogram ##y(x)##. Now I want to predict the number of counts at some other point, not in the original data, using this fitted function and assign an error to it.

Is the prediction ##y(x)##actually an integer number of counts at the value ##x## (whatever ##x## represents)? If the prediction predicts the parameter ##\lambda## of Poission distribution, it can be used to predict the

The Poisson Error is a type of statistical error that occurs when measuring the number of events that occur within a certain time period or area. It is based on the assumption that the events follow a Poisson distribution, which is a mathematical model for the probability of rare events.

Adding errors in quadrature is a method used to combine multiple sources of error in a measurement. It involves taking the square root of the sum of the squared errors from each source. This is done to obtain a more accurate estimate of the overall error.

The Poisson Error is most commonly used when counting discrete events, such as radioactive decay or the number of particles in a sample. It is also used in situations where the number of events is small and the probability of each event is low.

No, the Poisson Error is only applicable to discrete data. For continuous data, other types of errors such as standard deviation or standard error should be used.

The formula for calculating the Poisson Error is the square root of the number of events. However, this assumes that the number of events is large enough to approximate a normal distribution. If the number of events is small, a correction factor should be applied to the formula.

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