# How does TF1::GetRandom() work?

Hi guys,

can anyone explain to me how `TF1::GetRandom()` exactly works when called?

I don’t know if it’s only me, but the explanation given in the source code is very foggy, or maybe too much condensed.

I will appreciate any kind of help

Hi,
the `TF1::GetRandom()`of the TF1 extract a number using the TF1 function as a p.d.f.
In example I defined the TF1 as

`TF1 *f=new TF1("f","*x*exp(-x)",0,20)` and set the parameter  equal to 250

then i called 2000 times GetRandom to fill an histogram

`for( int i=0;i<2000;i++)h->Fill(f->GetRandom())`

and the result is the plot attached.(choosing the right scaling factors, the TF1 overlap with the histogram perfectly)

Cheers,
Stefano

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Hi Stefano,

Sorry for the misunderstanding, but with my questions I meant: “How does GetRandom() can give you random numbers following the function shape?”

The explanation given in the source file is the following:
The distribution contained in the function fname (TF1) is integrated over the channel contents.
It is normalized to 1. For each bin the integral is approximated by a parabola. The parabola coefficients are stored as non persistent data members Getting one random number implies:

• Generating a random number between 0 and 1 (say r1)
• Look in which bin in the normalized integral r1 corresponds to
• Evaluate the parabolic curve in the selected bin to find the corresponding X value.

This is what is not clear to me about GetRandom()

Thank you so much

Sorry for the late answer and the misunderstanding,
When you want to generate a random number according to a specific distribution, you have
to apply the Inverse transform sampling

• normalize the area of the distribution
• build the cumulative distribution (CDF), basically you integrate the the normalized function.
• the cumulative distribution for how is defined, span the y-axis the range [0,1] and is monotonically increasing
• randomly choose a number r1 between 0 and 1, you choose the y of the CDF, then to this y correspond only one x, and this x is distributed as the function you defined.

In simple case, as exponential distribution you are able to do all this analitically and obtain

``````x = log(1-r1)/(−λ)
``````

otherwise you have to do everything numerically with some approximation, and it is what root do.

I hope everything is understandable .

S

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Ok that’s clear, but what about the parabola mentioned in the description?

It’s just for the approximation of the cumulative and to easily compute the x from the y

Ok thank you, problem solved 