I’m trying to fit a gaussian to a set of data, but somehow I get an error. (i.e. first argument <<1>> in nonlinearmodelfit is not a list or a rectangular array). Does anyone know what’s going on? What is the proper way to use NonLinearModelFit command?
Look at the help page and carefully compare the form of your data with that or with this
In[1]:= data = Table[{x, E^-(x - 1)^2 + RandomReal[{-.1, .1}]}, {x, -2., 4., 1/10}]
Out[1]= {{-2., 0.0301034}, {-1.9, -0.0154798}, {-1.8, 0.022465}, {-1.7, 0.0010194}, {-1.6, -0.0295686},
{-1.5, -0.0952078}, {-1.4, 0.0208647}, {-1.3, 0.0503616}, {-1.2, 0.100381}, {-1.1, 0.0454354},
{-1., -0.0307495}, {-0.9, 0.00838033}, {-0.8, 0.0325882}, {-0.7, 0.0383335}, {-0.6, 0.0515882},
{-0.5, 0.0404762}, {-0.4, 0.0451534}, {-0.3, 0.0915646}, {-0.2, 0.217585}, {-0.1, 0.222667},
{0., 0.440198}, {0.1, 0.477472}, {0.2, 0.618511}, {0.3, 0.550046}, {0.4, 0.640443}, {0.5, 0.712902},
{0.6, 0.791899}, {0.7, 0.824463}, {0.8, 1.02962}, {0.9, 0.979843}, {1., 0.999929}, {1.1, 0.920938},
{1.2, 1.05641}, {1.3, 0.908881}, {1.4, 0.881643}, {1.5, 0.689059}, {1.6, 0.632981}, {1.7, 0.700848},
{1.8, 0.452774}, {1.9, 0.346829}, {2., 0.299357}, {2.1, 0.275064}, {2.2, 0.245725}, {2.3, 0.212584},
{2.4, 0.136231}, {2.5, 0.0869989}, {2.6, 0.109057}, {2.7, 0.128253}, {2.8, -0.00609724}, {2.9, 0.126926},
{3., 0.0669788}, {3.1, 0.0309545}, {3.2, 0.0471385}, {3.3, -0.0577374}, {3.4, 0.0613904}, {3.5, -0.0870592},
{3.6, -0.0039362}, {3.7, 0.0774653}, {3.8, -0.0933359}, {3.9, 0.00204892}, {4., -0.0526784}}
In[2]:= fun = Normal[NonlinearModelFit[data, E^-(x - a)^2, a, x]];
g = Show[ListPlot[data], Plot[fun, {x, -2, 4}]]
Do not use NonlinearModelFit for this purpose. This is a common mistake
If you want to fit some data to a statistical distribution, use a function like EstimatedDistribution.
Looks to me like EstimatedDistribution is designed to find the distribution of a list of numbers, not fit a list of ordered pairs to a distribution, which is how I interpret the original question, as did Bill.