So... I am working on part b and I haven no idea what this question is asking me to do. Does it want me to plot the actual Q(x) equation graph with part a graphs?
It appears as if you need to plot the pdf(x) and cdf(x) and compare to the estimated pdf and cdf you obtained for the different values of t.
Related
I am trying trying to graph the polynomial fit of a 2D dataset in Matlab.
This is what I tried:
rawTable = readtable('Test_data.xlsx','Sheet','Sheet1');
x = rawTable.A;
y = rawTable.B;
figure(1)
scatter(x,y)
c = polyfit(x,y,2);
y_fitted = polyval(c,x);
hold on
plot(x,y_fitted,'r','LineWidth',2)
rawTable.A and rawTable.A are randomly generated numbers. (i.e. the x dataset cannot be represented in the following form : x=0:0.1:100)
The result:
second-order polynomial
But the result I expect looks like this (generated in Excel):
enter image description here
How can I graph the second-order polynomial fit in MATLAB?
I sense some confusion regarding what the output of each of those Matlab function mean. So I'll clarify. And I think we need some details as well. So expect some verbosity. A quick answer, however, is available at the end.
c = polyfit(x,y,2) gives the coefficient vectors of the polynomial fit. You can get the fit information such as error estimate following the documentation.
Name this polynomial as P. P in Matlab is actually the function P=#(x)c(1)*x.^2+c(2)*x+c(3).
Suppose you have a single point X, then polyval(c,X) outputs the value of P(X). And if x is a vector, polyval(c,x) is a vector corresponding to [P(x(1)), P(x(2)),...].
Now that does not represent what the fit is. Just as a quick hack to see something visually, you can try plot(sort(x),polyval(c,sort(x)),'r','LineWidth',2), ie. you can first sort your data and try plotting on those x-values.
However, it is only a hack because a) your data set may be so irregularly spaced that the spline doesn't represent function or b) evaluating on the whole of your data set is unnecessary and inefficient.
The robust and 'standard' way to plot a 2D function of known analytical form in Matlab is as follows:
Define some evenly-spaced x-values over the interval you want to plot the function. For example, x=1:0.1:10. For example, x=linspace(0,1,100).
Evaluate the function on these x-values
Put the above two components into plot(). plot() can either plot the function as sampled points, or connect the points with automatic spline, which is the default.
(For step 1, quadrature is ambiguous but specific enough of a term to describe this process if you wish to communicate with a single word.)
So, instead of using the x in your original data set, you should do something like:
t=linspace(min(x),max(x),100);
plot(t,polyval(c,t),'r','LineWidth',2)
I am trying to obtain an equation for a function fitted to some histogram data, I was thinking of trying to do this by fitting a rational function as the data doesn't resemble any distribution recognisable by myself.
The data is experimental, and I want to be able to generate a random number according to its distribution. Hence I am hoping to be able to fit it to some sort of PDF from which I can obtain a CDF, which can be rearranged to a function into which a uniformly distributed random number between 0 and 1 can be substituted in order to obtain the desired result.
I have attempted to use the histfit function, which has worked but I couldn't figure out how to obtain an equation for the curve it fitted. Is there something stupid I have missed?
Update: I have discovered the function rationalfit, however I am struggling to figure out what the inputs need to be.
Further Update: Upon exploring the histfit command further I have discovered the option to fit it to a kernal, the figure for which looks promising, however I am only able to obtain a set of x and y values for the curve, not its equation as a I wanted.
From the documentation on histfit:
Algorithms
histfit uses fitdist to fit a distribution to data. Use fitdist
to obtain parameters used in fitting.
So the answer to your question is to use fitdist to get the parameters you're after. Here's the example from the documentation:
rng default; % For reproducibility
r = normrnd(10,1,100,1);
histfit(r)
pd = fitdist(r,'Normal')
pd =
NormalDistribution
Normal distribution
mu = 10.1231 [9.89244, 10.3537]
sigma = 1.1624 [1.02059, 1.35033]
Say for example I have data which forms the parabolic curve y=x^2, and I want to read off the x value for a given y value. How do I go about doing this in MATLAB?
If it were a straight line, I could just use the equation of the line of best fit to calculate easily, however I can't do this with a curved line. If I can't find a solution, I'll solve for roots
Thanks in advance.
If all data are arrays (not analytical expressions), I usually do that finding minimal absolute error
x=some_array;
[~,ind]=min(abs(x.^2-y0))
Here y0 is a given y value
If your data are represented by a function, you can use fsolve:
function y = myfun(x)
y=x^2-y0
[x,fval] = fsolve(#myfun,x0,options)
For symbolic computations, one can use solve
syms x
solve(x^2 - y0)
Assuming your two curves are just two vectors of data, I would suggest you use Fast and Robust Curve Intersections from the File Exchange. See also these two similar questions: how to find intersection points when lines are created from an array and Finding where plots may cross with octave / matlab.
I am trying to add Gaussian fit to the histogram in MATLAB, but I do not know how to apply the fit to one particular peak only.
http://postimg.org/image/phms61rdh/ first plot
http://postimg.org/image/sindrn8er/ second plot
I am also posting part of the code I have been using:
data_Rb = (importdata('path\name.txt'));
counts_Rb = data_Rb.data(:,3);
figure
hist(counts_Rb, nbins);
xlim([0 120]);
title('Rubidium');
histfit(counts_Rb,1000);
pd=fitdist(counts_Rb(:),'normal')
x=0:0.001:120;
PDF=pdf(pd,x); %PDF is a vector of y values: it's our fit
PDF=PDF/max(PDF); %nor
y=ylim;
PDF=PDF*y(2);
hold on
plot(x,PDF,'r-','LineWidth',2);
hold off
These two blocks give me two different Gaussians as shown in the first picture. I do not understand why they fit data so badly: is it because of the tail on the RHS?
In the second plot I need to apply Gaussian fit to the last peak only. How should I do it?
And finally, after applying the fit, fit results are outputed onto the screen. Is there a function to save them into an array or so for later use?
Thanks in advance!
Regarding your last question, see How can I access the fitted distribution parameters from the HISTFIT function in Statistiics Toolbox ?
There is a workaround for this isssue by making a copy of the HISTFIT
function and modifying the code to pass out the "pd" variable. One way
to do this is to change the "h" output on the first line of the code
to "varargout" and add the following to the end of the file:
h = [hh; hh1];
argout={h,pd};
if nargout > length(argout)
error('Too many output arguments.');
end
[varargout{1:nargout}]=argout{1:nargout};
Starting from the plot of one curve, it is possible to obtain the parametric equation of that curve?
In particular, say x={1 2 3 4 5 6....} the x axis, and y = {a b c d e f....} the corresponding y axis. I have the plot(x,y).
Now, how i can obtain the equation that describe the plotted curve? it is possible to display the parametric equation starting from the spline interpolation?
Thank you
If you want to display a polynomial fit function alongside your graph, the following example should help:
x=-3:.1:3;
y=4*x.^3-5*x.^2-7.*x+2+10*rand(1,61);
p=polyfit(x,y,3); %# third order polynomial fit, p=[a,b,c,d] of ax^3+bx^2+cx+d
yfit=polyval(p,x); %# evaluate the curve fit over x
plot(x,y,'.')
hold on
plot(x,yfit,'-g')
equation=sprintf('y=%2.2gx^3+%2.2gx^2+%2.2gx+%2.2g',p); %# format string for equation
equation=strrep(equation,'+-','-'); %# replace any redundant signs
text(-1,-80,equation) %# place equation string on graph
legend('Data','Fit','Location','northwest')
Last year, I wrote up a set of three blogs for Loren, on the topic of modeling/interpolationg a curve. They may cover some of your questions, although I never did find the time to add another 3 blogs to finish the topic to my satisfaction. Perhaps one day I will get that done.
The problem is to recognize there are infinitely many curves that will interpolate a set of data points. A spline is a nice choice, because it can be made well behaved. However, that spline has no simple "equation" to write down. Instead, it has many polynomial segments, pieced together to be well behaved.
You're asking for the function/mapping between two data sets. Knowing the physics involved, the function can be derived by modeling the system. Write down the differential equations and solve it.
Left alone with just two data series, an input and an output with a 'black box' in between you may approximate the series with an arbitrary function. You may start with a polynomial function
y = a*x^2 + b*x + c
Given your input vector x and your output vector y, parameters a,b,c must be determined applying a fitness function.
There is an example of Polynomial Curve Fitting in the MathWorks documentation.
Curve Fitting Tool provides a flexible graphical user interfacewhere you can interactively fit curves and surfaces to data and viewplots. You can:
Create, plot, and compare multiple fits
Use linear or nonlinear regression, interpolation,local smoothing regression, or custom equations
View goodness-of-fit statistics, display confidenceintervals and residuals, remove outliers and assess fits with validationdata
Automatically generate code for fitting and plottingsurfaces, or export fits to workspace for further analysis