is there codes that helps to find out the type of the distribution ?

i have a set of data of a certain parameter that i need to know the statistical distribution belong to, is there any way or codes can help?

Answer 1

[Rik]

No. What you ask is fundamentally impossible.

What you can do is try several distributions and see how well they fit.

[Walter Roberson]

For example

d = sum(randi(6, 2, 100));
histogram(d)

[h, p] = ttest(d, 7)

h = 0

p = 0.1957

A return of 0 means that it is not possible to reject the hypothesis that d is normally distributed with mean 7.

But knowing the way that d was constructed, we know that d is not normally distributed: d is strictly integer-valued and d does not have infinite tails, so d cannot possibly be normally distributed.

Thus it is difficult to say specifically that a distribution of data is a particular distribution; it is much easier to say "there is a low probability that it is not this distribution."

[Khaled aL Qattawi]

thanks

[Mohamed Zied]

Thank you for your answer.

I plotted many PDFs (using the distributionFitter tool) as you can see in the attached scrreenshot.

Is the judgement of the best fit graphical?

In my case for example, is the Lognormal distribution the best fit to my Data.

Thank you in advance.

[Rik]

What exactly is the best fit depends on your domain knowledge. Your data looks like a skewed normal distribution to me (or the superposition of two). What makes sense in your situation is not something I can tell you, but you need to tell me. And that would answer your own question.

Answer 2

[John D'Errico]

As Rik said, difficult to know which distribution a random variable comes from. Don't believe me?

x = 0.96489;

Do you know if that number was generated from a uniform distribution? On what range? Was it from a normal distribution? A beta? Lognormal? Gamma? Weibull? Exponential? Poisson? Rayleigh? Lots more.

Even had I given you more data, you still cannot know. You can perform tests to see if one distribution would be more likely than another. (More data would be REALLY helpful then.)

You can use tools to fit a family of distributions. Common ones are the Johnson or Pearson family of distributions. Even then you won't KNOW which distribution a sample came from, only making a better guess. There are tools like fitdist and distributionFitter. I thought I remember the stats toolbox having a tool to fit the pearson family of distributions too. Ah, yes, it does, though I had to look. pearsrnd does it all.

The nice thing about the Pearson family (and the Johnson family as I recall) is they encompass a pretty wide variety of distribution shapes. But I have a funny feeling one can abuse them if you don't understand these things. And those tools are completely dependent on estimates of the first 4 moments of your distributino, but the higher order moments are difficult to estimate well.

Anyway, the fact is, almost NO data you will generate in the real world comes from a truly KNOWN distribution. All data will be corrupted in some way, so that even if it should be essentially normal, you will always have crap in there that makes it not quite normal, etc.

[Khaled aL Qattawi]

yes i see, thanks a lot