CDF(cumulative distribution function) starts not from 0
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I have a dataset, then i want to know the distribution, i used exppdf(X,mu), but the result is not reasonable, please see the figure, why the CDF(cumulative distribution function) starts not from 0? And the PDF(probability density function) seems too small. How can i solve this problem?
2 Comments
Greig
on 21 Sep 2015
The reason that the PDF and CDF don't start at zero probability is because the distributions that you specify exist outside of the X values you used.
These two functions generate the theoretical PDFs and CDFs for the specified distributions at the X values you input. They are not for data fitting.
See my answer below for more details.
Answers (2)
Greig
on 21 Sep 2015
It seems like your choice of parametric distribution is not appropriate for your data and it seems that you might be approaching the problem in the wrong way.
First things first... What are your data? What is their physical meaning? Do they have lower or upper bounds? What do you want to do with the distribution fit? Have previous analyses (by others) justified the use of a exponential or chi-squared distribution? All of these questions will help you to decide what type of distribution is appropriate to fit to your data.
Second things second, fitting... Do you have Statistics Toolbox? If so, then dfittool is a good place to start. In command window type
doc 'Model Data Using the Distribution Fitting App'
and choose the first option.
If you can provide us with more info about your data we can probably help some more.
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Xiaowei Wang
on 21 Sep 2015
3 Comments
Greig
on 22 Sep 2015
The point I was trying to make above, is that you need to understand the physics behind what you are measuring to try and decide what distribution is appropriate. I don't know what your data are, so you are in the best position to know the properties of the data and the physical constraints that they are subject to. These properties and constraints tell you what distribution is appropriate.
At quick glance you are looking at directivity? Which, according to the Wikipedia page is the ratio of radiative intensity in one direction (U) to the average across all directions (P). Is that correct?
I know nothing about this, so the following might be wrong. But, I am guess that U >= 0, and assuming at least one direction has some power, P > 0. So this means that the smallest possible value is 0, and the largest is infinity. This range is known as the supported range of a distribution.
What are the units of your data? Have you transformed them in dB? Trusted Wikipedia says this is more common. If so, this will change the supported range of the distribution to [-infinity , infinity]. Other distributions found on the Wikipedia link above will then be more appropriate.
Maybe you can think of other properties of the data that will help to constrain what is a reasonable distribution. I guess both U and P will be subject to some noise or calculation, this may mean they themselves follow a distribution. In this case directivity may be the ratio of two distributions, which sometimes has a nice defined form (but not always).
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