How can obtain the probability density function for a random discreate set of data and fit a custom distribution function ??

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Surendra Ratnu 2023-12-8

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评论： Surendra Ratnu 2023-12-14

temp_data.xlsx

I have random data. I want to calculate the probability density function. I also fit a custom distribution function which is the

where gamma is the gamma function of n and n is the distribution parameter and x is the variable.

I attached the data. Can you provide the solution for this ??

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Torsten 2023-12-8

编辑：Torsten 2023-12-8

Seems to be the Gamma Distribution with a = b:

https://www.fmrib.ox.ac.uk/datasets/techrep/tr03tb1/tr03tb1/node24.html

Surendra Ratnu 2023-12-9

编辑：Surendra Ratnu 2023-12-9

@Paul It is true P(n,x) = 0 for x<0.

@Torsten yes.

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Torsten 2023-12-8

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编辑：Torsten 2023-12-8

Use "histogram" to plot the empirical probability density function for your data and use "mle" to estimate n.

https://uk.mathworks.com/help/matlab/ref/matlab.graphics.chart.primitive.histogram.html

https://uk.mathworks.com/help/stats/mle.html

Why are there so many data repeated multiple times ? Did you create them artificially ?

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Torsten 2023-12-13

在 MATLAB Online 中打开

temp_data.xlsx

x = xlsread('temp_data.xlsx');

pdf = @(x,n)n^n/gamma(n) * x.^(n-1) .* exp(-n*x);

[phat,pci] = mle(x,'pdf',pdf,'Start',1)

phat = 3.3776

pci = 2×1

3.1120 3.6431

hold on

h = histogram(x);

h.Normalization = 'pdf';

y = linspace(0,max(x),100);

plot(y,pdf(y,phat))

hold off

Surendra Ratnu 2023-12-14

Thank you for your inout. It's works. How can i know the goodness of the distribution fit if i fit using mle??

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John D'Errico 2023-12-12

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编辑：John D'Errico 2023-12-12

在 MATLAB Online 中打开

temp_data.xlsx

Can you write custom code to fit a PDF to data? Yes. It is not that truly difficult, if you know what you are doing. HOWEVER, SHOULD you write custom code to fit a PDF using maximum likelihood estimation? NO. It already exists in MATLAB, Use those codes. Writing your own code to do something already provided to you is a bad idea. If you don't have a clue what you are doing and don't have the skills in such things, then your result will be poor. Use code provided to you by professionals. Even there, you can have problems if you use the code incorrectly or provide it bad data that does not fit the distribution, but at least you give yourself a chance of success.

Now, does your data have a problem? YES. It is not at all random looking. In fact, what you have is not even a set of samples from a distribution, but apparently a cumulative histogram of sorts.

x = xlsread('temp_data.xlsx');

plot(x)

In there I see what appears to be stairsteps in your "data". So these are not samples from a continuous distribution. For example, the first 54 points in that vector are identical. It is not clear how you generated this data, which you claim to have measured.

So first, you need to explain what you have in that data set. How you created it.

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Surendra Ratnu 2023-12-13

Actually, Data are droplet size of the spray. I measured the drop size of spray using some software. The spray created identical drop size that why the data are in repeatative manner.