<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html>
  <head>
  <meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">

<title>Two component error model — sigma_twocomp • mkin</title>

<!-- jquery -->
<script src="https://code.jquery.com/jquery-3.1.0.min.js" integrity="sha384-nrOSfDHtoPMzJHjVTdCopGqIqeYETSXhZDFyniQ8ZHcVy08QesyHcnOUpMpqnmWq" crossorigin="anonymous"></script>
<!-- Bootstrap -->

<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-BVYiiSIFeK1dGmJRAkycuHAHRg32OmUcww7on3RYdg4Va+PmSTsz/K68vbdEjh4u" crossorigin="anonymous">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script>

<!-- Font Awesome icons -->
<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" integrity="sha384-T8Gy5hrqNKT+hzMclPo118YTQO6cYprQmhrYwIiQ/3axmI1hQomh7Ud2hPOy8SP1" crossorigin="anonymous">

<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/1.7.1/clipboard.min.js" integrity="sha384-cV+rhyOuRHc9Ub/91rihWcGmMmCXDeksTtCihMupQHSsi8GIIRDG0ThDc3HGQFJ3" crossorigin="anonymous"></script>

<!-- sticky kit -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/sticky-kit/1.1.3/sticky-kit.min.js" integrity="sha256-c4Rlo1ZozqTPE2RLuvbusY3+SU1pQaJC0TjuhygMipw=" crossorigin="anonymous"></script>

<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>



<meta property="og:title" content="Two component error model — sigma_twocomp" />

<meta property="og:description" content="Function describing the standard deviation of the measurement error 
  in dependence of the measured value \(y\):
$$\sigma = \sqrt{ \sigma_{low}^2 + y^2 * {rsd}_{high}^2}$$
This is the error model used for example by Werner et al. (1978). The model
  proposed by Rocke and Lorenzato (1995) can be written in this form as well,
  but assumes approximate lognormal distribution of errors for high values of y." />
<meta name="twitter:card" content="summary" />



<!-- mathjax -->
<script src='https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></script>

<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->


  </head>

  <body>
    <div class="container template-reference-topic">
      <header>
      <div class="navbar navbar-default navbar-fixed-top" role="navigation">
  <div class="container">
    <div class="navbar-header">
      <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar">
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
      </button>
      <span class="navbar-brand">
        <a class="navbar-link" href="../index.html">mkin</a>
        <span class="label label-default" data-toggle="tooltip" data-placement="bottom" title="Released package">0.9.47.6</span>
      </span>
    </div>

    <div id="navbar" class="navbar-collapse collapse">
      <ul class="nav navbar-nav">
        <li>
  <a href="../reference/index.html">Functions and data</a>
</li>
<li class="dropdown">
  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
    Articles
     
    <span class="caret"></span>
  </a>
  <ul class="dropdown-menu" role="menu">
    <li>
      <a href="../articles/mkin.html">Introduction to mkin</a>
    </li>
    <li>
      <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
    </li>
    <li>
      <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
    </li>
    <li>
      <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
    </li>
    <li>
      <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
    </li>
    <li>
      <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
    </li>
  </ul>
</li>
<li>
  <a href="../news/index.html">News</a>
</li>
      </ul>
      
      <ul class="nav navbar-nav navbar-right">
        
      </ul>
      
    </div><!--/.nav-collapse -->
  </div><!--/.container -->
</div><!--/.navbar -->

      
      </header>

<div class="row">
  <div class="col-md-9 contents">
    <div class="page-header">
    <h1>Two component error model</h1>
    
    <div class="hidden name"><code>sigma_twocomp.Rd</code></div>
    </div>

    <div class="ref-description">
    
    <p>Function describing the standard deviation of the measurement error 
  in dependence of the measured value \(y\):</p>
<p>$$\sigma = \sqrt{ \sigma_{low}^2 + y^2 * {rsd}_{high}^2}$$</p>
<p>This is the error model used for example by Werner et al. (1978). The model
  proposed by Rocke and Lorenzato (1995) can be written in this form as well,
  but assumes approximate lognormal distribution of errors for high values of y.</p>
    
    </div>

    <pre class="usage"><span class='fu'>sigma_twocomp</span>(<span class='no'>y</span>, <span class='no'>sigma_low</span>, <span class='no'>rsd_high</span>)</pre>
    
    <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
    <table class="ref-arguments">
    <colgroup><col class="name" /><col class="desc" /></colgroup>
    <tr>
      <th>y</th>
      <td><p>The magnitude of the observed value</p></td>
    </tr>
    <tr>
      <th>sigma_low</th>
      <td><p>The asymptotic minimum of the standard deviation for low observed values</p></td>
    </tr>
    <tr>
      <th>rsd_high</th>
      <td><p>The coefficient describing the increase of the standard deviation with 
    the magnitude of the observed value</p></td>
    </tr>
    </table>
    
    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>

    <p>The standard deviation of the response variable.</p>
    
    <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>

    <p>Werner, Mario, Brooks, Samuel H., and Knott, Lancaster B. (1978)
  Additive, Multiplicative, and Mixed Analytical Errors. Clinical Chemistry
  24(11), 1895-1898.</p>
<p>Rocke, David M. and Lorenzato, Stefan (1995) A two-component model for
  measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
    

  </div>
  <div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
    <h2>Contents</h2>
    <ul class="nav nav-pills nav-stacked">
      <li><a href="#arguments">Arguments</a></li>
      
      <li><a href="#value">Value</a></li>

      <li><a href="#references">References</a></li>
          </ul>

  </div>
</div>

      <footer>
      <div class="copyright">
  <p>Developed by Johannes Ranke.</p>
</div>

<div class="pkgdown">
  <p>Site built with <a href="http://pkgdown.r-lib.org/">pkgdown</a>.</p>
</div>

      </footer>
   </div>

  

  </body>
</html>