B4J Question (math) calculating an integral

[MegatenFreak]

Hello.
There's a math calculation I need to do. It begins with a function f(x) which I've already managed; however, the next step states:
"Find the integral, from -infinity to x, of the previous value." (I used the word 'infinity' instead of the actual symbol)
Is there anyway that could be done using the available math functions and libraries?
Thanks a lot in advance.

 

[Erel]

What is f(x)?

Calculating a numerical integral is quite simple, however if you know f(x) you can find the integral directly.
A library will not help here.

 

[MegatenFreak]

Well, this is the whole formula:

All the stuff between the integral sign and "dt" can be easily calculated. All the variables are clear.
I realize this is not a math forum! I was just wondering if there is any way I can calculate the result of this for a given set of variables. It's something I need to calculate for a laboratory information system. It determines how accurate the results of a test are.

 

[Erel]

Sub AppStart (Args() As String)
    Log(CalcIntegral(-10000, 5000))
End Sub

Private Sub CalcIntegral(FromValue As Double, ToValue As Double) As Double
    Dim u As Double = 10
    Dim o As Double = 64
    Dim e2 As Double = Power(cE, -1/2)
    Dim denominator As Double = Sqrt(2 * cPI * o)
    Dim delta As Double = 0.001
    Dim Result As Double = 0 'C
    Dim t as Double
    For t = FromValue To ToValue Step delta
        Dim i As Double = Power(e2, Power((t - u) / o, 2)) / denominator
'        Log(i)
        Result = Result + i * delta
    Next
    Return Result
End Sub

Maybe I did a mistake but it looks like it converges to sqrt(o).

 

[MegatenFreak]

Wow! I did a few adjustments to fix the primary formula, and the result is actually close to the desired value, based on some examples!
You're amazing! That math is totally beyond me!
Speed could be an issue, though, especially since the 'from' value has to be really low (to simulate -infinity).
I'll try creating a ready-made EXCEL look-up table and load it into my app.
Thanks Erel.

 

[Erel]

The only "real" math here is:

 Result = Result + i * delta

1. Test it in release mode.
2. Make some tests on the FromValue. It will quickly become insignificant.
3. Also try it with different deltas. I just made this one up and ran it.

 

[MegatenFreak]

I tested with other FromValue and delta values. I think I got the right combo for a speedy calculation close enough to the result I want.
Quite honestly, I had given up on this one! You're a life-saver! Thanks again

 

[klaus]

The equation is the normal distribution curve.

Below my routine:

'Normal distribution integral
'BeginValue and EndValue are the interval values
'Mu = mean value
'Sigma = standard deviation
'Delta = calculation interval
Private Sub CalcGaussIntegral(BeginValue As Double, EndValue As Double, Mu As Double, Sigma As Double, Delta As Double) As Double
    Private i, Integral, y0, y1 As Double
    Private Denominator As Double
  
    Delta = 0.1
    Denominator = Sqrt(2 * cPI)
    y0 = Power(cE, -(BeginValue - Mu) * (BeginValue - Mu) / 2 / Sigma / Sigma) / Sigma / Denominator
  
    For i = BeginValue + Delta To EndValue Step Delta
        y1 = Power(cE, -(i - Mu) * (i - Mu) / 2 / Sigma / Sigma) / Sigma / Denominator
        Integral = Integral + (y0 + y1) / 2 * Delta
        y0 = y1
    Next
    Return Integral
End Sub

The routine uses the trapeze integration formula.

With
CalcGaussIntegral(-5, 5, 0, 1, 0.001) you get 1, 100%
CalcGaussIntegral(-5, 0, 0, 1, 0.001) you get 0.5, 50%
CalcGaussIntegral(-1.96, 1.96, 0, 1, 0.001) you get 0.95, 95%

Maybe the calculation of the interval of confidence might be of interest for you.

Sorry, I am not as fast as Erel.

EDIT:

And the shape of the normal distribution curve and its integral drawn with xGraph.
Example corresponding to these parameters: CalcGaussIntegral(-5, 5, 0, 1, 0.001)

 

[MegatenFreak]

You're right, Klaus. It is indeed the normal distribution curve formula, which, strangely, is used for an entirely different purpose.
The only certified source of calculation this procedure has mentioned (in the ISO standard documents) is by using the Excel NORMDIST function. (for example, NORMDIST(3.0, 2.7, 0.2, TRUE). I got to that integral formula from microsoft office's explanation of excel formulas.
Thanks a lot Klaus. Your explanations made things clearer. I'm currently discussing it with the project's technical expert to see just how 'exact' he needs the answer to be. If going as far as 2 fractions is enough, a lookup table will do the job.

 

[derez]

See this library https://www.b4x.com/android/forum/threads/probability-library.15681/post-88945 , the calculation there is using a polinom which gives the result very close to the actual value - right away. It works for B4J as well.
The code for stdNorm is shown as an example in post #4 there.

 

[MegatenFreak]

Cool. I'll check it out. Thanks