XProfan

English

p.specht

The Gauss-distribution is by the known Glockenkurve given. asks one, How probably one incident over one designed Grenzwert To lying comes, then comes it on The expanse under the Glocke ex this Grenzwert on.

Flächen under Kurven go mathematically as Integralfunktion displayed. Integrale yield itself often as further, relatively slight To ermittelnde Formeln - dummerweise straight in the entrapment the Gaußglocke but not!
usually must then numerische Lösungsverfahren since (z.B. through abschnittsweises Aufaddieren of Trapezflächen, into one The curve hacking has), circa a vaguely worth this Gauß-Integrals To determined. the appear in the practice often To costly, and one begnügt itself with relatively simply To berechenden Näherungsformeln, The but only in a eingeschränkten Wertebereich count.

The umgekehrte question, Namely for a pretended probability (=Fläche) jenen vorgenannten Grenzwert To detect, can then duch Umstellung so of/ one Näherungsformel on The others Variable determined go. the nachstehende Program does very the. one speaks then from the "Inversen Gaussfunktion". pretended becomes The expanse (= probability), out comes the sought Grenzwert, from the from until worth "+Unendlich" these expanse the Gaussglocke cut becomes.

Compile Mark Separation

Window Title "Formel for Inverse the Normalverteilungsintegrals"
' fountain: https://jean-pierre.moreau.pagesperso-orange.fr/Basic/invnorm_bas.txt
' Transponiert to XProfan 11.2a (D) demonstration by P.woodpecker, Vienna/Austria
' No warranty whatsoever! No Gewähr, for garnix!
'****************************************************
'* Program to demonstrate inverse normal subroutine *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'*                                                  *
'*  P(Z>X)     X                                    *
'* ----------------                                 *
'*  0.50    0.0000                                  *
'*  0.48    0.0500                                  *
'*  0.46    0.1002                                  *
'*  0.44    0.1507                                  *
'*  0.42    0.2015                                  *
'*  0.40    0.2529                                  *
'*  0.38    0.3050                                  *
'*  0.36    0.3580                                  *
'*  0.34    0.4120                                  *
'*  0.32    0.4673                                  *
'*  0.30    0.5240                                  *
'*  0.28    0.5825                                  *
'*  0.26    0.6430                                  *
'*  0.24    0.7060                                  *
'*  0.22    0.7719                                  *
'*  0.20    0.8414                                  *
'*  0.18    0.9152                                  *
'*  0.16    0.9944                                  *
'*  0.14    1.0804                                  *
'*  0.12    1.1751                                  *
'*  0.10    1.2817                                  *
'*  0.08    1.4053                                  *
'*  0.06    1.5551                                  *
'*  0.04    1.7511                                  *
'*  0.02    2.0542                                  *
'*                                                  *
'****************************************************
'DEFINT I-n
'DEFDBL A-H, O-Z
Declare i&,x!,y!,from!,to!,step!
CLS
PRINT
Print " the Program accounts a Näherung on the Integral the Gaussverteilung,"
Print "And of course The expanse between x and +Inf (rights Page!). moreover becomes to  "
Print " Abramowitz/Stegun one Rationales Polynom using. pretended becomes y, the "
Print " zugehörige X moreover becomes accounts. "
Print " for y within [0 ... 0,5] is the accuracy rather as 0.0005"
Print
PRINT " P(Z>X)     X  "
PRINT "----------------"
from!=0.5:to!=0:step! = -0.02
y!=from!
i&=1

Repeat

    s1000' Proc-appeal
    Case x!<0.000001:x!=0
    PRINT stature$(" 0.## ",y!),tab(12),stature$("0.####",x!)
    Casenote i& Mod 15: WaitInput
    inc i&
    y!=y!+step!

Until y!<to!

PRINT
WaitInput
END

Proc s1000

    '***********************************************
    '*   Inverse normal distribution subroutine    *
    '* ------------------------------------------- *
    '* Diese program calculates on approximation to *
    '* the integral of the normal distribution     *
    '* function from x to infinity (the tail).     *
    '* A rational polynomial is used. The input is *
    '* in y, with the result returned in x. The    *
    '* accuracy is better then 0.0005 in the brat *
    '* 0 < y < 0.5.                                *
    '* ------------------------------------------- *
    '* Reference: Abramowitz and Stegun.           *
    '***********************************************
    'Define coefficients
    Declare c0!,c1!,c2!,d1!,d2!,d3!,z!
    c0! = 2.515517
    c1! = 0.802853
    c2! = 0.010328
    d1! = 1.432788
    d2! = 0.189269
    d3! = 0.001308
    Case y!=0:x!=1E13
    Case y!=0:Return
    z!=Sqrt(-1*Ln(Sqr(y!)))
    x! = 1+d1!*z!+d2!*Sqr(z!)+ d3!*z!*Sqr(z!)
    x! = (c0!+c1!*z!+c2!*Sqr(z!))/x!
    x! = z!-x!

ENDPROC

'End of file invnorm.prf