statistics - Extract parameter after fitting from Poisson distribution -

i bit confused in poisson distribution. fitting poisson type distribution , need extract mean , error on mean. know poisson distribution

in root (c/c++ based analysis framework) defined function below

function = ( [0]  * power( [1] / [2]  ,  x/[2] )  * exp (-[1]/[2]) ) /     gamma(x/[2] + 1)  : [0] = normalizing parameter         [1] / [2] -> mean (mu)          x / [2] -> x         gamma( x / [2] + 1 ) = factorial (x / [2]) 

so, in principle mean of poisson distribution mu = 1/2 , error standard deviation square root of mean.

but, if using value mean coming around 10 , hence error ~3.

while mean of distribution around 2 (as can see) confused. because parameter 1 's value coming out around 2 or 3. so, should use parameter 1 mean value or what??

please suggest should use , why?

my full code below:

th1f *hclustersize = new th1f("hclustersize","cluster size ge1/1", 10,0.,10.);     tmptree->draw("g1ycl.ngeoch>>hclustersize","g1ycl@.getentries()==1 && g1xcl@.getentries()==1");     hclustersize->getxaxis()->settitle("cluster size");     hclustersize->getyaxis()->settitle("#entries");     tf1 *f1 = new tf1("f1","[0]*tmath::power(([1]/[2]),(x/[2]))*(tmath::exp(-([1]/[2])))/tmath::gamma((x/[2])+1)", 0, 10);      f1->setparameters(hclustersize->getmaximum(), hclustersize->getmean(), 1);      hclustersize->fit("f1"); // use option "r" = fit between "xmin" , "xmax" of "f1" 

on root command line fitting poisson distribution can done this:

tf1* func = new tf1("mypoi","[0]*tmath::poisson(x,[1])",0,20)                           func->setparameter(0,5000) // set starting values                                       func->setparameter(1,2.) // set starting values                                         func->setparname(0,"normalisation") func->setparname(1,"#mu") th1f* hist = new th1f("hist","hist",20,-0.5,19.5)   (int = 0 ; < 5000 ; i++) { hist->fill(grandom->poisson(3.5)); } hist->draw()         hist->fit(func)      

note that bin centers shifted wrt initial post, such bin center of 0 counts @ 0 , not @ 0.5 (and same other bins).