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## [Help-gsl] very naive question: how to fit _correctly_ an histogram ?

**From**: |
Jerome BENOIT |

**Subject**: |
[Help-gsl] very naive question: how to fit _correctly_ an histogram ? |

**Date**: |
Thu, 22 Jan 2009 03:18:21 +0800 |

**User-agent**: |
Mozilla-Thunderbird 2.0.0.19 (X11/20090103) |

Hello List,
I have a collection of histograms got from simulations to fit.
I want to perform nonlinear least-squares fits.
My concern is rather how to parametrise in a relevant way the a priori model
function of my choice, and how to extract in a pertinent way the information
from the histogram.
First, let say that the model function is a Gaussian:
g0(x;sigma)=exp(-x^2/sigma^2/2)/(sqrt(2Pi)*sigma))
Of course my histogram may be not centered, so beside
the scale sigma, a shift xi may be considered.
The model function then becomes
g1(x;xi,sigma)=exp(-(x-xi)^2/sigma^2/2)/(sqrt(2Pi)*sigma)=g0(x-xi;sigma).

`Following the same idea, a coefficient Alpha may be introduced:
``g2(x;Alpha,xi,sigma)=Alpha*g1(x;xi,sigma)=Alpha*g0(x-xi;sigma).
`
Second, what about the observed value G_i for the ith bin centered at x_i ?
G_i=(width of the bin)*(number of element inside the bin)/(sum over the bins of
G_i)
Finally, the function component to implement to feed GSL (section 37.1) may
write:
f_i=(G_i-g2(x_i;Alpha,xi,sigma)*(with of the bin))/(weight_i)
[by the way, how to get meaning full weight_i ?].
My questions are quite naive, but so far, I have found no totally satisfying
answer.
By googling I have found a lot of fuzzy how to, but no explicit one:
does any know where a fully histogram least-squares fit example can be found
in literature or/and on the web ?
Thanks in advance,
Jerome
--
Jerome BENOIT
jgmbenoit_at_mailsnare_dot_net

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