Using pdf to find threshold

Hello,

I am trying to determine a threshold for data that is p>0.05. The data is very positively skewed but I am unsure how to use or interpret the pdf() function to determine a threshold value. I want apply a 'Rayleigh'distribution but how do you choose the values for the input parameter B? I read the documentation but it does not give detailed explanation on how to choose these parameters. I've numeric matrix of example data. This is my code so far:

load('sample')
pd = fitdist(sample,'Rayleigh')

pd = 
  RayleighDistribution

  Rayleigh distribution
    B = 0.0844953   [0.0830468, 0.0859955]

x_values = 0:.01:.5;
y = pdf(pd,x_values);
plot(x_values,y)

But the next step is finding the threshold value which I am unsure how to do.

Thank you for your help!

[Torsten]

I am trying to determine a threshold for data that is p>0.05.

Could you explain in more detail what you mean here ?

Answer 1

[Jeff Miller]

I'm not entirely sure what you mean by "threshold", but maybe you are trying to identify the middle 95% of the distribution? If that is the case, then

>> icdf(pd,0.025)
ans =
     0.019013
>> icdf(pd,0.975)
ans =
      0.22951

tells you that scores less than 0.019013 are in the bottom 2.5% and scores greater than 0.22951 are in the top 2.5%, so the middle 95% is the range in between there. Alternatively, if you just want the bottom 95% then you would use

>> icdf(pd,0.95)
ans =
      0.20682

the "icdf" function returns the value X of the distribution such that the indicated proportion is less than X.

hth,

[Carly]

Yes, that works perfectly! Thank you!

Answer 2

[Image Analyst]

For skewed distributions such as that, the triangle method works well. Function is attached.