title: non-central chi-square probability and non-centrality parameter
body: <p>How can I get the value of the non-centrality parameter that gives a probability of exactly 0.9 for different critical values and degrees of freedom? </p>
  
  <p>For example, with the significance level = 0.05 and 1 degree of freedom (critical value = 3.84), the ncp must be equal to 10.50742 in order to get a probability of 0.9:    </p>
  
  <pre><code>1 - pchisq(3.841459, 1, 10.50742)
  [1] 0.9
  </code></pre>