I've plotted a histogram of some data. Here it is http://dl.dropbox.com/u/54057365/All/departure%20time.JPG
How can remove the gaps between the bars? Should I be using a histogram? But how can you normalize the measurements on the y axis in a histogram?
DepartureTimes = load('Departure Times (hr).txt') h = hist(DepartureTimes,24); h = h/sum(h); bar(h, 'DisplayName', 'Depature Times'); legend('show'); xlim([5 25])
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Hi John, if you type "help hist", you'll find information about specifying the bar centers. This implicitly controls the width of the bins that the bars cover.
If you want to change the gap between the bars, see "help hist" for information about returning the bar heights instead of plotting them, and "help bar" for information about drawing bars and controlling the space between them.
X = randn(1e3,1); N = hist(X,22); bar(N,1);
As far as whether the histogram is appropriate or how to "normalize" it. Can you be more specific? People generally plot a histogram in two ways:
1.) the raw frequency or count histogram 2.) a probability histogram (as you have almost done), so that they can overlay a PDF for comparison.
Here's an example of that (requires Statistics Toolbox):
Data = randn(1000,1); %just making up some junk data binWidth = 0.7; %This is the bin width binCtrs = -3:0.7:3; %Bin centers, depends on your data n=length(Data); counts = hist(Data,binCtrs); prob = counts / (n * binWidth); H = bar(binCtrs,prob,'hist'); set(H,'facecolor',[0.5 0.5 0.5]); % get the N(0,1) pdf on a finer grid hold on; x = -3:.1:3; y = normpdf(x,0,1); %requires Statistics toolbox plot(x,y,'k','linewidth',2);
yes, you are doing the correct thing. You can use dfittool to fit a Gamma distribution, which you can use estimate the parameters of a chi-square PDF.
dfittool will also overlay the fitted pdf on the data.
The alpha parameter in a gamma is dof/2 and the beta parameter is 2.
You can generate code for your fit from dfittool and export the fit to the workspace.
I'm saying that if you fit a gamma, you get an alpha and a beta parameter. You can use that to see if a chi-square is appropriate (and not a more general gamma) and if so, get the dof parameter.
R = chi2rnd(5,1e3,1); %chi-square 5 dof phat = mle(R,'distribution','Gamma');
phat(1) is the alpha parameter, but that is the dof/2 for a chi- square
Gives you an estimate of the dof parameter for a chi-square.
phat(2) should always be close to 2 (if it isn't that is a indication that chi-square is not a good fit)
You can also use fitdist()
pd = fitdist(R,'gamma');
For this example, I get:
a = 2.50903 b = 1.99592
which indicates a chi-square PDF with 5 dof.
To remove the gaps between the bars, you set the ' BarWidth ' property to 1:
bar(binsNumbers, CountData, 'BarWidth', 1);
By setting the BarWidth to between 0 and 1 you can go from having huge gaps between the bars (very skinny bars) to having full width bars (bars touch each other with no gap at all).
I have a question, I know it has been some time since the last post in this thread but I am posting it here since it is relevant... How do you obtained the goodness of fit of gamma distrubution fitted to any data? For example the chi^2 or the R^2 value maybe using chi2gof or something similar?
Thanks for your help. Harish