<html>

  <head>
    <title>
      TOMS462 - Bivariate Normal Distribution
    </title>
  </head>

  <body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">

    <h1 align = "center">
      TOMS462 <br> Bivariate Normal Distribution
    </h1>

    <hr>

    <p>
      <b>TOMS462</b> 
      is a FORTRAN77 library which 
      evaluates the upper right tail of the bivariate normal distribution; that is,
      the probability that normal variables X and Y with correlation R will
      satisfy H <= X and K <= Y.
    </p>

    <p>
      The text of many ACM TOMS algorithms is available online
      through ACM:
              <a href = "http://www.acm.org/pubs/calgo/">
                         http://www.acm.org/pubs/calgo</a>
      or NETLIB:
      <a href = "http://www.netlib.org/toms/index.html">
      http://www.netlib.org/toms/index.html</a>.
    </p>

    <h3 align = "center">
      Usage:
    </h3>

    <p> 
      <dl>
        <dt>
          value = <b>bivnor ( ah, ak, r )</b>
        </dt>
        <dd>
          computes <b>VALUE</b>, the probability that two variables,
          <i>X</i> and <i>Y</i> related by a bivariate normal distribution
          with correlation <b>R</b>, satisfy <b>AH</b> &lt;= <i>X</i> and
          <b>AK</b> &lt;= <i>Y</i>.
        </dd>
      </dl>
    </p>

    <h3 align = "center">
      Languages:
    </h3>

    <p>
      <b>TOMS462</b> is available in
      <a href = "../../c_src/toms462/toms462.html">a C version</a> and
      <a href = "../../cpp_src/toms462/toms462.html">a C++ version</a> and
      <a href = "../../f77_src/toms462/toms462.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/toms462/toms462.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/toms462/toms462.html">a MATLAB version</a>.
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../f77_src/owens/owens.html">
      OWENS</a>,
      a FORTRAN77 library which
      evaluates Owen's T function.
    </p>

    <p>
      <a href = "../../f_src/prob/prob.html">
      PROB</a>,
      a FORTRAN90 library which
      contains a
      number of routines for evaluating cumulative distribution functions.
    </p>

    <p>
      <a href = "../../f77_src/test_values/test_values.html">
      TEST_VALUES</a>,
      a FORTRAN77 library which
      supplies test values of various mathematical functions.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

    <p>
      <ol>
        <li>
          Thomas Donnelly,<br>
          Algorithm 462: Bivariate Normal Distribution,<br>
          Communications of the ACM,<br>
          October 1973, Volume 16, Number 10, page 638.
        </li>
        <li>
          Donald Owen,<br>
          Tables for Computing Bivariate Normal Probabilities,<br>
          Annals of Mathematical Statistics,<br>
          Volume 27, Number 4, pages 1075-1090, December 1956.
        </li>
      </ol>
    </p>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "toms462.f">toms462.f</a>, the source code.
        </li>
        <li>
          <a href = "toms462.csh">toms462.csh</a>,
          commands to compile the source code.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "toms462_prb.f">toms462_prb.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "toms462_prb.csh">toms462_prb.csh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "toms462_prb_output.txt">toms462_prb_output.txt</a>,
          the output from a run of the sample program.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>BIVNOR</b> computes the bivariate normal CDF.
        </li>
        <li>
          <b>BIVARIATE_NORMAL_CDF_VALUES</b> returns some values of the bivariate normal CDF.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f77_src.html">
      the FORTRAN77 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 25 May 2009.
    </i>

    <!-- John Burkardt -->

  </body>

  <!-- Initial HTML skeleton created by HTMLINDEX. -->

</html>
