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cdfnor(1) Scilab Function cdfnor(1)
NAME
cdfnor - cumulative distribution function normal distribution
CALLING SEQUENCE
[P,Q]=cdfnor("PQ",X,Mean,Std)
[X]=cdfnor("X",Mean,Std,P,Q)
[Mean]=cdfnor("Mean",Std,P,Q,X)
[Std]=cdfnor("Std",P,Q,X,Mean)
PARAMETERS
P,Q,X,Mean,Std
: six real vectors of the same size.
P,Q (Q=1-P)
: The integral from -infinity to X of the normal density. Input
range: (0,1].
X :Upper limit of integration of the normal-density. Input range:
( -infinity, +infinity)
Mean : The mean of the normal density. Input range: (-infinity,
+infinity)
Sd : Standard Deviation of the normal density. Input range: (0,
+infinity).
DESCRIPTION
Calculates any one parameter of the normal distribution given values for
the others.
A slightly modified version of ANORM from Cody, W.D. (1993). "ALGORITHM
715: SPECFUN - A Portabel FORTRAN Package of Special Function Routines and
Test Drivers" acm Transactions on Mathematical Software. 19, 22-32. is
used to calulate the cumulative standard normal distribution.
The rational functions from pages 90-95 of Kennedy and Gentle, Statisti-
cal Computing, Marcel Dekker, NY, 1980 are used as starting values to
Newton's Iterations which compute the inverse standard normal. Therefore
no searches are necessary for any parameter.
For X < -15, the asymptotic expansion for the normal is used as the start-
ing value in finding the inverse standard normal. This is formula 26.2.12
of Abramowitz and Stegun.
The normal density is proportional to exp( - 0.5 * (( X - MEAN)/SD)**2)
From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Func-
tions, Inverses, and Other Parameters (February, 1994) Barry W. Brown,
James Lovato and Kathy Russell. The University of Texas.
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