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FindFit with BinCounts or a bar chart in Mathematica

daList={62.8347, 88.5806, 74.8825, 61.1739, 66.1062, 42.4912, 62.7023, 
        39.0254, 48.3332, 48.5521, 51.5432, 69.4951, 60.0677, 48.4408, 
        59.273, 30.0093, 94.6293, 43.904, 59.6066, 58.7394, 68.6183, 83.0942, 
        73.1526, 47.7382, 75.6227, 58.7549, 59.2727, 26.7627, 89.493, 
        49.3775, 79.9154, 73.2187, 49.5929, 84.4546, 28.3952, 75.7541, 
        72.5095, 60.5712, 53.2651, 33.5062, 80.4114, 63.7094, 90.2438, 
        55.2248, 44.437, 28.1884, 4.77477, 36.8398, 70.3579, 28.1913, 
        43.9001, 23.8907, 12.7823, 22.3473, 57.6724, 49.0148}

The above is an example of the evidence I'm dealing with. I use BinCounts, but this is just to illustrate the visual histogram that should do this: I would like to fit the shape of this histogram

Histogram@data

enter image description here

I know how to fit the data points themselves, for example:

model = 0.2659615202676218` E^(-0.2222222222222222` (x - \[Mu])^2)
FindFit[data, model, \[Mu], x]

Which is far from what I wanted to do: how can I put a bin count / histogram in Mathematica?

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1 answer

If you have a MMA V8, you can use the new DistributionFitTest

disFitObj = DistributionFitTest[daList, NormalDistribution[a, b],"HypothesisTestData"];

Show[
   SmoothHistogram[daList], 
   Plot[PDF[disFitObj["FittedDistribution"], x], {x, 0, 120}, 
        PlotStyle -> Red
   ], 
   PlotRange -> All
]

enter image description here

disFitObj["FittedDistributionParameters"]

(* ==> {a -> 55.8115, b -> 20.3259} *)

disFitObj["FittedDistribution"]

(* ==> NormalDistribution[55.8115, 20.3259] *)

It can also match other distributions.

V8 - HistogramList, Histogram binning. Histogram.

{bins, counts} = HistogramList[daList]

(* ==> {{0, 20, 40, 60, 80, 100}, {2, 10, 20, 17, 7}} *)

centers = MovingAverage[bins, 2]

(* ==> {10, 30, 50, 70, 90} *)

model = s E^(-((x - \[Mu])^2/\[Sigma]^2));

pars = FindFit[{centers, counts}\[Transpose], 
                     model, {{\[Mu], 50}, {s, 20}, {\[Sigma], 10}}, x]

(* ==> {\[Mu] -> 56.7075, s -> 20.7153, \[Sigma] -> 31.3521} *)

Show[Histogram[daList],Plot[model /. pars // Evaluate, {x, 0, 120}]]

enter image description here

NonlinearModeFit . , , .

V7 HistogramList, , this:

fh [, bspec, fh] : {{ [b, 1], [b, 2]}, { [b, 2], [b, 3]}, [Ellipsis]} { [c, 1], [c, 2], [Ellipsis]}. , [c, i].

( ):

Reap[Histogram[daList, Automatic, (Sow[{#1, #2}]; #2) &]][[2]]

(* ==> {{{{{0, 20}, {20, 40}, {40, 60}, {60, 80}, {80, 100}}, {2, 
    10, 20, 17, 7}}}} *)

, BinCounts, MMA. binning:

counts = BinCounts[daList, {0, Ceiling[Max[daList], 10], 10}]

(* ==>  {1, 1, 6, 4, 11, 9, 9, 8, 5, 2} *)

centers = Table[c + 5, {c, 0, Ceiling[Max[daList] - 10, 10], 10}]

(* ==>  {5, 15, 25, 35, 45, 55, 65, 75, 85, 95} *)

pars = FindFit[{centers, counts}\[Transpose],
                model, {{\[Mu], 50}, {s, 20}, {\[Sigma], 10}}, x]

(* ==> \[Mu] -> 56.6575, s -> 10.0184, \[Sigma] -> 32.8779} *)

Show[
   Histogram[daList, {0, Ceiling[Max[daList], 10], 10}], 
   Plot[model /. pars // Evaluate, {x, 0, 120}]
]

enter image description here

, . , I, s, . , , s.

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