Fixing a FindRoot error - what does it mean?

Questions
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1

Hi everyone,

I do hope someone will be able to help me. I have some density function of which I want to calculate some percentage points for arbitrary parameters. I want to do this in Mathematica - with using the function “FindRoot”. It does however give me the following error:

"FindRoot::nlnum: “The function value {False} is not a list of numbers with dimensions {1} at {z} = {1.`}.”

I don’t even know where to start to look for a solution! The code that I am using have been used by myself before, but only know it is giving me a problem. Any thoughts? Code attached in the Mathematica .nb file.

What the program is supposed to do:

There is a defined density funciton, called WGen. It is a univariate function of z, with 5 parameters (n1, n2, r, rho, th1 and th2).

This density function’s integral up to some point z is then calculated to “mimic” its distribution function (CDF).
Then, the function “h” is defined as the CDF minus the critical point - and this function is then solved for = 0 (effectively solving CDF = p). I wish to get the value of z which will result in the CDF being equal to p.

Thanks guys, I’ll really appreciate any constructive thoughts. I’m not that well aquainted with Mathematica so I’m also still learning.

2

The reason for the error is that h[10, 12, 2, 0.5, 3, 5, 0.01, z] (where z does not have a numerical value) returns a ConditionalExpression. Try something like

In[8]:= cdf[n1_, n2_, r_, rho_, th1_, th2_, z_] := 
   Integrate[WGen[n1, n2, r, rho, th1, th2, t], {t, 0, z}, Assumptions -> z > 0]

In[9]:= FindRoot[h[10, 12, 2, 0.5, 3, 5, 0.01, z] == 0, {z, 1}]

Out[9]= {z -> 0.178494}