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Trailing-Edge - PDP-10 Archives - decuslib20-02 - decus/20-0026/ndtri.doc
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SUBROUTINE NDTRI

PURPOSE
  COMPUTES X = P**(-1)(Y), THE ARGUMENT X SUCH THAT Y= P(X) =
  THE PROBABILITY THAT THE RANDOM VARIABLE U, DISTRIBUTED
  NORMALLY(0,1), IS LESS THAN OR EQUAL TO X.  F(X), THE
  ORDINATE OF THE NORMAL DENSITY, AT X, IS ALSO COMPUTED.

USAGE
  CALL NDTRI(P,X,D,IER)

DESCRIPTION OF PARAMETERS
  P   - INPUT PROBABILITY.
  X   - OUTPUT ARGUMENT SUCH THAT P = Y = THE PROBABILITY THAT
	   U, THE RANDOM VARIABLE, IS LESS THAN OR EQUAL TO X.
  D   - OUTPUT DENSITY, F(X).
  IER - OUTPUT ERROR CODE
	= -1 IF P IS NOT IN THE INTERVAL (0,1), INCLUSIVE.
	  X=D=.99999E+74 IN THIS CASE
	= 0 IF THERE IS NO ERROR.  SEE REMARKS, BELOW.

REMARKS
  MAXIMUM ERROR IS 0.00045.
  IF P = 0, X IS SET TO -(10)**74.  D IS SET TO 0.
  IF P = 1, X IS SET TO  (10)**74.  D IS SET TO 0.

SUBROUTINES AND SUBPROGRAMS REQUIRED
  NONE

METHOD
  BASED ON APPROXIMATIONS IN C. HASTINGS, APPROXIMATIONS FOR
  DIGITAL COMPUTERS, PRINCETON UNIV. PRESS, PRINCETON, N.J.,
  1955.  SEE EQUATION 26.2.23, HANDBOOK OF MATHEMATICAL
  FUNCTIONS, ABRAMOWITZ AND STEGUN, DOVER PUBLICATIONS, INC.,
  NEW YORK.