Hi, first of all, This is my first post so sorry if I am doing anything wrong-please let me know if I do so I can fix it in the next time.

Now for the problem: I have created a distribution as follows:

    gauss[\[Sigma]_, Nelec_, Nevents_][S2_] := 
      Nevents/Sqrt[2 \[Pi] Nelec*\[Sigma]^2] E^(- (S2 - Nelec)^2/(
       2 Nelec \[Sigma]^2));
    histo0 := {0, 3, 2, 0, 2, 0, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 2,
        0, 0, 0, 0, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 0, 0, 1, 1, 0, 0, 1};
    totali[S2_] := 
      Sum[gauss[\[Sigma], n, histo0[[n - 2]] + dn[n - 3]][S2], {n, 4, 
        42}];
    int=Integrate[totali[S2], {S2, 2, 47}];
    MyDis = ProbabilityDistribution[totali[S2]/int, {S2, 2, 47}];

Basically, What I did is sum a few Gaussian distributions, where the mean is a natural number between 4 and 42, and the standard deviation is a positive variable $\sigma$ times the square root of the mean. Each gaussian distribution is multiplied by a non-negetive integer, where histo0 is my initial guess, and dn[n] is "how wrong" I am. I want to fit the parameters to the following data:

MyData := {3.55, 3.929612637855687`, 4.198861253938525`, 
   4.772217586600313`, 4.86366648742909`, 6.766448860938332`, 
   6.948322072316817`, 8.89701146228973`, 9.409033926355143`, 
   9.636778566425097`, 13.261158408037534`, 15.582422423427438`, 
   17.146213657293824`, 22.437562769783195`, 22.47612166533075`, 
   26.751597041651493`, 28.015997164367814`, 28.107911510263797`, 
   30.27938610839986`, 31.15744941537931`, 31.88040495283035`, 
   33.0687273993196`, 33.50485819234863`, 33.813167859728125`, 
   35.66914520018869`, 39.14112642715986`, 40.4114737998406`, 
   42.51464449681805`};

However, It is crucial that "dn" will remain integers. I can use $\sigma$=0.23, but I'd rather claculate it from the fit. When I took $\sigma$=0.23, I tried using:

 FindDistributionParameters[MyData, 
  MyDis, {{dn[1], 0}, {dn[2], 0}, {dn[3], 0}, {dn[4], 0}, {dn[5], 
    0}, {dn[6], 0}, {dn[7], 0}, {dn[8], 0}, {dn[9], 0}, {dn[10], 
    0}, {dn[11], 0}, {dn[12], 0}, {dn[13], 0}, {dn[14], 0}, {dn[15], 
    0}, {dn[16], 0}, {dn[17], 0}, {dn[18], 0}, {dn[19], 0}, {dn[20], 
    0}, {dn[21], 0}, {dn[22], 0}, {dn[23], 0}, {dn[24], 0}, {dn[25], 
    0}, {dn[26], 0}, {dn[27], 0}, {dn[28], 0}, {dn[29], 0}, {dn[30], 
    0}, {dn[31], 0}, {dn[32], 0}, {dn[33], 0}, {dn[34], 0}, {dn[35], 
    0}, {dn[36], 0}, {dn[37], 0}, {dn[38], 0},{dn[39],0}}, AccuracyGoal -> 0, 
  PrecisionGoal -> 0]

But it just gave me zeros. I also tried with the accuracy goal goes to 1, and that did not give me integers. Is there any way to determine the best "dn"s, from the region {-2,-1,0,1,2}, while taking a positive sigma smaller than 1? Thanks In advance.