I would like to create a tool for generating a stochastic time-series distribution, for which I can provide the parameters (for a normal distribution) the mean, standard deviation, skewness and kurtosis. There is a similar question here using R, but I am not able to interpret this and put it in MATLAB.
Is there something that someone knows can do this already? (I haven't been able to find anything)
If not, what would be some good advice for starting something of my own? Any known useful functions? I would also like to be able to build upon it afterwards, for example: adding outliers, clusters of volatility, adjusting heteroscedasticity.
I realise me saying 'stochastic' and then in the same sentence 'given parameters' may seem odd, but it isn't - I want each time point to be random, but the parameters to describe, say 10,000 time points.
If you're looking for the equivalent of the solution in R, Matlab's Statistics Toolbox has limited support for the Johnson and Pearson distribution systems. In particular, the johnsrnd function produces random variates for the Johnson system. The Pearson system and pearsrnd, however, takes moments directly.
A big caveat. Using moments to describe or fit or produce random variates – often referred to as moment matching – is not robust and poorly regarded by statisticians. They're not guaranteed to uniquely define a distribution unless you have the entire moment generating function.
Related
I have been looking for a Matlab function that can do a nonlinear total least square fit, basically fit a custom function to data which has errors in all dimensions. The easiest case being x and y data-points with different given standard deviations in x and y, for every single point. This is a very common scenario in all natural sciences and just because most people only know how to do a least square fit with errors in y does not mean it wouldn't be extremely useful. I know the problem is far more complicated than a simple y-error, this is probably why most (not even physicists like myself) learned how to properly do this with multidimensional errors.
I would expect that a software like matlab could do it but unless I'm bad at reading the otherwise mostly useful help pages I think even a 'full' Matlab license doesn't provide such fitting functionality. Other tools like Origin, Igor, Scipy use the freely available fortran package "ODRPACK95", for instance. There are few contributions about total least square or deming fits on the file exchange, but they're for linear fits only, which is of little use to me.
I'd be happy for any hint that can help me out
kind regards
First I should point out that I haven't practiced MATLAB much since I graduated last year (also as a Physicist). That being said, I remember using
lsqcurvefit()
in MATLAB to perform non-linear curve fits. Now, this may, or may not work depending on what you mean by custom function? I'm assuming you want to fit some known expression similar to one of these,
y = A*sin(x)+B
y = A*e^(B*x) + C
It is extremely difficult to perform a fit without knowning the form, e.g. as above. Ultimately, all mathematical functions can be approximated by polynomials for small enough intervals. This is something you might want to consider, as MATLAB does have lots of tools for doing polynomial regression.
In the end, I would acutally reccomend you to write your own fit-function. There are tons of examples for this online. The idea is to know the true solution's form as above, and guess on the parameters, A,B,C.... Create an error- (or cost-) function, which produces an quantitative error (deviation) between your data and the guessed solution. The problem is then reduced to minimizing the error, for which MATLAB has lots of built-in functionality.
I have been all over Google trying to find a good function/package to perform multivariate regression (i.e. predict multiple continuous variables given another set of multiple continuous variables).
I wish to use something like fitlm(), since that also gives me p-value statistics and R squared statistics. Does anything like that exist?
Matlab has a bundle of tools for this, see this page.
I believe that mvregress is the most rounded and mainstream tool. See this page for setting up an analysis with it.
Also, a comment in this post may be useful for alternatives, if needed: it is possible to approach this via separate regression analyses, one for each response variable.
I've been looking around scipy and sklearn for clustering algorithms for a particular problem I have. I need some way of characterizing a population of N particles into k groups, where k is not necessarily know, and in addition to this, no a priori linking lengths are known (similar to this question).
I've tried kmeans, which works well if you know how many clusters you want. I've tried dbscan, which does poorly unless you tell it a characteristic length scale on which to stop looking (or start looking) for clusters. The problem is, I have potentially thousands of these clusters of particles, and I cannot spend the time to tell kmeans/dbscan algorithms what they should go off of.
Here is an example of what dbscan find:
You can see that there really are two separate populations here, though adjusting the epsilon factor (the max. distance between neighboring clusters parameter), I simply cannot get it to see those two populations of particles.
Is there any other algorithms which would work here? I'm looking for minimal information upfront - in other words, I'd like the algorithm to be able to make "smart" decisions about what could constitute a separate cluster.
I've found one that requires NO a priori information/guesses and does very well for what I'm asking it to do. It's called Mean Shift and is located in SciKit-Learn. It's also relatively quick (compared to other algorithms like Affinity Propagation).
Here's an example of what it gives:
I also want to point out that in the documentation is states that it may not scale well.
When using DBSCAN it can be helpful to scale/normalize data or
distances beforehand, so that estimation of epsilon will be relative.
There is a implementation of DBSCAN - I think its the one
Anony-Mousse somewhere denoted as 'floating around' - , which comes
with a epsilon estimator function. It works, as long as its not fed
with large datasets.
There are several incomplete versions of OPTICS at github. Maybe
you can find one to adapt it for your purpose. Still
trying to figure out myself, which effect minPts has, using one and
the same extraction method.
You can try a minimum spanning tree (zahn algorithm) and then remove the longest edge similar to alpha shapes. I used it with a delaunay triangulation and a concave hull:http://www.phpdevpad.de/geofence. You can also try a hierarchical cluster for example clusterfck.
Your plot indicates that you chose the minPts parameter way too small.
Have a look at OPTICS, which does no longer need the epsilon parameter of DBSCAN.
I have a curve which looks roughly / qualitative like the curves displayed in those 3 images.
The only thing I know is that the first part of the curve is hardware-specific supposed to be a linear curve and the second part is some sort of logarithmic part (might be a combination of two logarithmic curves), i.e. linlog camera. But I couldn't tell the mathematic structure of the equation, e.g. wether it looks like a*log(b)+c or a*(log(c+b))^2 etc. Is there a way to best fit/find out a good regression for this type of curve and is there a certain way to do this specifically in MATLAB? :-) I've got the student version, i.e. all toolboxes etc.
fminsearch is a very general way to find best-fit parameters once you have decided on a parametric equation. And the optimization toolbox has a range of more-sophisticated ways.
Comparing the merits of one parametric equation against another, however, is a deep topic. The main thing to be aware of is that you can always tweak the equation, adding another term or parameter or whatever, and get a better fit in terms of lower sum-squared-error or whatever other goodness-of-fit metric you decide is appropriate. That doesn't mean it's a good thing to keep adding parameters: your solution might be becoming overly complex. In the end the most reliable way to compare how well two different parametric models are doing is to cross-validate: optimize the parameters on a subset of the data, and evaluate only on data that the optimization procedure has not yet seen.
You can try the "function finder" on my curve fitting web site zunzun.com and see what it comes up with - it is free. If you have any trouble please email me directly and I'll do my best to help.
James Phillips
zunzun#zunzun.com
This might be a silly question! I have a array P which represents the probability distribution of some data e.g. [0;0.3;0.7] How can I determine the type or class of discrete probability distribution of P? The original data is unavailable to me.
dfittool or fitdist requires me to give the data as input, while I already have its probability distribution. Any ideas?
You probably might have seen different probability distributions during lecture or your reading. All you have to do is plotting the given distribution against the candidates. As the distributions itself are parametrized, curve fitting or trial end error come into play. The distribution with the least error, best fit, might be the one you are looking for.
It is not possible to find out a priori what kind of distribution some data (especially with as low n as in your example) is coming from.
If you have an idea of the process that generated your data, you might be able to get an idea of which distributions to test. Maybe your data comes from the family of gamma distributions, maybe your data comes from the family of Weibull distributions etc. Then, you can fit these general distributions and see whether they are likely to simplify to a more common distribution.
For a visual representation of how well your data could approximate a certain distribution, you can use PROBPLOT.
Once you have identified possible distributions, you can fit them to the data and use the Bayesian Information Criterion (BIC) to compare which fit describes the data best. Note that unless you have huge numbers of noise-free data, it is impossible to tell which fit is correct if you have several possible distributions with comparatively low BIC.