I have a 1x4225 vector that its elements are between 0 and 1 and I want to plot their probability density function in matlab.
In the case of ksdensity() the problem is that the probability sometimes gets more than 1.
I also tried the code below to do that:
A= [1x4225];
xRange = 0:1;
N = hist(A,xRange);
plot(xRange,N./numel(A))
But because of huge number of my data it made an ambiguous plot that consists of some vertical lines and is useless for me.
So is there any way to solve this problem or any other way to do this in matlab that shows each element as a separate point in pdf plot ?
When you do xRange = 0:1; you get a 2-element vector [0 1]. That is probably not what you want. Specify a step like:
xRange = 0:0.01:1;
Plotting each element as a point is accomplished in MATLAB with the line specifier argument, like plot(xRange,N./numel(A),'*'). However, for a histogram with only a small number of bins, you might be better off with bar(...). If you go with a finer step, then plotting might be better.
Related
I've been using interp1 to plot curves to follow sets of datapoints, and for most of the datapoints it's been working:
But when I try it with another set of datapoints it doesn't follow them at all:
For both interpolations the code I'm using is just:
curve = interp1(x, y, 'pchip');
Where x is just a set of numbers that correspond to the x axis of each datapoint, and y is the values themselves.
I can't tell what is different about the second dataset that is causing the interp1 function to not follow the data.
So with thanks to #m.s. for providing his code, it turns out the issue is that with the second graph I was interpolating with x= -90:10:90, whereas if I interpolate with 1:19, in a similar manner to the first graph, then the problem is fixed.
The figure shown above is the plot of cumulative distribution function (cdf) plot for relative error (attached together the code used to generate the plot). The relative error is defined as abs(measured-predicted)/(measured). May I know the possible error/interpretation as the plot is supposed to be a smooth curve.
X = load('measured.txt');
Xhat = load('predicted.txt');
idx = find(X>0);
x = X(idx);
xhat = Xhat(idx);
relativeError = abs(x-xhat)./(x);
cdfplot(relativeError);
The input data file is a 4x4 matrix with zeros on the diagonal and some unmeasured entries (represent with 0). Appreciate for your kind help. Thanks!
The plot should be a discontinuous one because you are using discrete data. You are not plotting an analytic function which has an explicit (or implicit) function that maps, say, x to y. Instead, all you have is at most 16 points that relates x and y.
The CDF only "grows" when new samples are counted; otherwise its value remains steady, just because there isn't any satisfying sample that could increase the "frequency".
You can check the example in Mathworks' `cdfplot1 documentation to understand the concept of "empirical cdf". Again, only when you observe a sample can you increase the cdf.
If you really want to "get" a smooth curve, either 1) add more points so that the discontinuous line looks smoother, or 2) find any statistical model of whatever you are working on, and plot the analytic function instead.
I have to plot 10 frequency distributions on one graph. In order to keep things tidy, I would like to avoid making a histogram with bins and would prefer having lines that follow the contour of each histogram plot.
I tried the following
[counts, bins] = hist(data);
plot(bins, counts)
But this gives me a very inexact and jagged line.
I read about ksdensity, which gives me a nice curve, but it changes the scaling of my y-axis and I need to be able to read the frequencies from the y-axis.
Can you recommend anything else?
You're using the default number of bins for your histogram and, I will assume, for your kernel density estimation calculations.
Depending on how many data points you have, that will certainly not be optimal, as you've discovered. The first thing to try is to calculate the optimum bin width to give the smoothest curve while simultaneously preserving the underlying PDF as best as possible. (see also here, here, and here);
If you still don't like how smooth the resulting plot is, you could try using the bins output from hist as a further input to ksdensity. Perhaps something like this:
[kcounts,kbins] = ksdensity(data,bins,'npoints',length(bins));
I don't have your data, so you may have to play with the parameters a bit to get exactly what you want.
Alternatively, you could try fitting a spline through the points that you get from hist and plotting that instead.
Some code:
data = randn(1,1e4);
optN = sshist(data);
figure(1)
[N,Center] = hist(data);
[Nopt,CenterOpt] = hist(data,optN);
[f,xi] = ksdensity(data,CenterOpt);
dN = mode(diff(Center));
dNopt = mode(diff(CenterOpt));
plot(Center,N/dN,'.-',CenterOpt,Nopt/dNopt,'.-',xi,f*length(data),'.-')
legend('Default','Optimum','ksdensity')
The result:
Note that the "optimum" bin width preserves some of the fine structure of the distribution (I had to run this a couple times to get the spikes) while the ksdensity gives a smooth curve. Depending on what you're looking for in your data, that may be either good or bad.
How about interpolating with splines?
nbins = 10; %// number of bins for original histogram
n_interp = 500; %// number of values for interpolation
[counts, bins] = hist(data, nbins);
bins_interp = linspace(bins(1), bins(end), n_interp);
counts_interp = interp1(bins, counts, bins_interp, 'spline');
plot(bins, counts) %// original histogram
figure
plot(bins_interp, counts_interp) %// interpolated histogram
Example: let
data = randn(1,1e4);
Original histogram:
Interpolated:
Following your code, the y axis in the above figures gives the count, not the probability density. To get probability density you need to normalize:
normalization = 1/(bins(2)-bins(1))/sum(counts);
plot(bins, counts*normalization) %// original histogram
plot(bins_interp, counts_interp*normalization) %// interpolated histogram
Check: total area should be approximately 1:
>> trapz(bins_interp, counts_interp*normalization)
ans =
1.0009
Am trying to plot 2 variable of different size length in matlab GUI using push button,
but because the variables are of different length it will not work,is there a way i can make it to plot.
d= pdist([x,y,z],'euclidean') ; % value of my distance
dd= 1:10:d; % interval and end 'd' value
FSL=-120; %value of free space loss get from the GUI
DFSL= 1:10:FSL %interval and end at FSL value
plot(dd,DFSL)
The plot code didnt work coming back with an error "
Error using plot
Vectors must be the same lengths"
You can plot vectors of two different lengths, but not against each other. You have used the syntax
plot(x,y)
which means for every element in vector x, there should be a corresponding element in vector y. In your case, you do not have this, hence the error.
You can plot like this though:
plot(x)
figure;
plot(y)
If you are looking to plot them in a single plot, subplot will be useful.
I have a Matlab figure I want to use in a paper. This figure contains multiple cdfplots.
Now the problem is that I cannot use the markers because the become very dense in the plot.
If i want to make the samples sparse I have to drop some samples from the cdfplot which will result in a different cdfplot line.
How can I add enough markers while maintaining the actual line?
One method is to get XData/YData properties from your curves follow solution (1) from #ephsmith and set it back. Here is an example for one curve.
y = evrnd(0,3,100,1); %# random data
%# original data
subplot(1,2,1)
h = cdfplot(y);
set(h,'Marker','*','MarkerSize',8,'MarkerEdgeColor','r','LineStyle','none')
%# reduced data
subplot(1,2,2)
h = cdfplot(y);
set(h,'Marker','*','MarkerSize',8,'MarkerEdgeColor','r','LineStyle','none')
xdata = get(h,'XData');
ydata = get(h,'YData');
set(h,'XData',xdata(1:5:end));
set(h,'YData',ydata(1:5:end));
Another method is to calculate empirical CDF separately using ECDF function, then reduce the results before plotting with PLOT.
y = evrnd(0,3,100,1); %# random data
[f, x] = ecdf(y);
%# original data
subplot(1,2,1)
plot(x,f,'*')
%# reduced data
subplot(1,2,2)
plot(x(1:5:end),f(1:5:end),'r*')
Result
I know this is potentially unnecessary given MATLAB's built-in functions (in the Statistics Toolbox anyway) but it may be of use to other viewers who do not have access to the toolbox.
The empirical CMF (CDF) is essentially the cumulative sum of the empirical PMF. The latter is attainable in MATLAB via the hist function. In order to get a nice approximation to the empirical PMF, the number of bins must be selected appropriately. In the following example, I assume that 64 bins is good enough for your data.
%# compute a histogram with 64 bins for the data points stored in y
[f,x]=hist(y,64);
%# convert the frequency points in f to proportions
f = f./sum(f);
%# compute the cumulative sum of the empirical PMF
cmf = cumsum(f);
Now you can choose how many points you'd like to plot by using the reduced data example given by yuk.
n=20 ; % number of total data markers in the curve graph
M_n = round(linspace(1,numel(y),n)) ; % indices of markers
% plot the whole line, and markers for selected data points
plot(x,y,'b-',y(M_n),y(M_n),'rs')
verry simple.....
try reducing the marker size.
x = rand(10000,1);
y = x + rand(10000,1);
plot(x,y,'b.','markersize',1);
For publishing purposes I tend to use the plot tools on the figure window. This allow you to tweak all of the plot parameters and immediately see the result.
If the problem is that you have too many data points, you can:
1). Plot using every nth sample of the data. Experiment to find an n that results in the look you want.
2). I typically fit curves to my data and add a few sparsely placed markers to plots of the fits to differentiate the curves.
Honestly, for publishing purposes I have always found that choosing different 'LineStyle' or 'LineWidth' properties for the lines gives much cleaner results than using different markers. This would also be a lot easier than trying to downsample your data, and for plots made with CDFPLOT I find that markers simply occlude the stairstep nature of the lines.