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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>cdfnor</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>Dec 1997</DATE>
  <SHORT_DESCRIPTION name="cdfnor"> cumulative distribution function normal distribution</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[P,Q]=cdfnor(&quot;PQ&quot;,X,Mean,Std)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[X]=cdfnor(&quot;X&quot;,Mean,Std,P,Q)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[Mean]=cdfnor(&quot;Mean&quot;,Std,P,Q,X)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[Std]=cdfnor(&quot;Std&quot;,P,Q,X,Mean)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>P,Q,X,Mean,Std</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: six real vectors of the same size.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>P,Q (Q=1-P)  </PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: The integral from -infinity to X of the normal density. Input range: (0,1].</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>X</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:Upper limit of integration of the normal-density. Input range: ( -infinity, +infinity)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>Mean</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:  The mean of the normal density. Input range: (-infinity, +infinity)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>Sd</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:  Standard Deviation of the normal density. Input range: (0, +infinity).</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    Calculates any one parameter of the normal
    distribution given values for the others.</P>
    <P>
    A slightly modified version of ANORM from
    Cody, W.D. (1993). &quot;ALGORITHM 715: SPECFUN - A Portabel FORTRAN
    Package of Special Function Routines and Test Drivers&quot;
    acm Transactions on Mathematical Software. 19, 22-32.
    is used to calulate the  cumulative standard normal distribution.</P>
    <P>
    The rational functions from pages  90-95  of Kennedy and Gentle,
    Statistical  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.</P>
    <P>
    For X &lt; -15, the asymptotic expansion for the normal is used  as
    the starting value in finding the inverse standard normal.
    This is formula 26.2.12 of Abramowitz and Stegun.</P>
    <P>
    The normal density is proportional to
    exp( - 0.5 * (( X - MEAN)/SD)**2)</P>
    <P>
    From DCDFLIB: Library of Fortran Routines for Cumulative Distribution
    Functions, Inverses, and Other Parameters (February, 1994)
    Barry W. Brown, James Lovato and Kathy Russell. The University of
    Texas.</P>
  </DESCRIPTION>
</MAN>
