F-Distribution

Functions > Statistics > Probability Distributions > F-Distribution

F-Distribution

The following functions are associated with the F-distribution equation:

Click to copy this expression

<region id="ID0EKODAB" top="76.800000000000011" left="57.600000000000009" height="77.2" width="355.32666666666671" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="1">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <mult />
      <apply>
        <div />
        <apply>
          <mult />
          <apply>
            <mult />
            <apply>
              <pow />
              <id xml:space="preserve">d1</id>
              <apply>
                <mult />
                <real>0.5</real>
                <id xml:space="preserve">d1</id>
              </apply>
            </apply>
            <apply>
              <pow />
              <id xml:space="preserve">d2</id>
              <apply>
                <mult />
                <real>0.5</real>
                <id xml:space="preserve">d2</id>
              </apply>
            </apply>
          </apply>
          <apply>
            <id xml:space="preserve">Γ</id>
            <apply>
              <div />
              <apply>
                <plus />
                <id xml:space="preserve">d1</id>
                <id xml:space="preserve">d2</id>
              </apply>
              <real>2</real>
            </apply>
          </apply>
        </apply>
        <apply>
          <mult />
          <apply>
            <id xml:space="preserve">Γ</id>
            <apply>
              <mult />
              <real>0.5</real>
              <id xml:space="preserve">d1</id>
            </apply>
          </apply>
          <apply>
            <id xml:space="preserve">Γ</id>
            <apply>
              <mult />
              <real>0.5</real>
              <id xml:space="preserve">d2</id>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <div />
        <apply>
          <pow />
          <id xml:space="preserve">x</id>
          <apply>
            <scale />
            <real>0.5</real>
            <parens>
              <apply>
                <minus />
                <id xml:space="preserve">d1</id>
                <real>2</real>
              </apply>
            </parens>
          </apply>
        </apply>
        <apply>
          <pow />
          <parens>
            <apply>
              <plus />
              <id xml:space="preserve">d2</id>
              <apply>
                <mult />
                <id xml:space="preserve">d1</id>
                <id xml:space="preserve">x</id>
              </apply>
            </apply>
          </parens>
          <apply>
            <scale />
            <real>0.5</real>
            <parens>
              <apply>
                <plus />
                <id xml:space="preserve">d1</id>
                <id xml:space="preserve">d2</id>
              </apply>
            </parens>
          </apply>
        </apply>
      </apply>
    </apply>
  </math>
</region>

• dF(x, d1, d2)—Returns the probability density for value x.

• pF(x, d1, d2)—Returns the cumulative probability distribution for value x.

• qF(p, d1, d2)—Returns the inverse cumulative probability distribution for probability p.

• rF(m, d1, d2)—Returns a vector of m random numbers having the F-distribution.

Arguments

• x is a scalar or vector of real values, x ≥ 0. To allow integration and other operations over this argument, values outside of the stated range are allowed, but they produce a 0 result.

• d1, d2 are positive integers representing the degrees of freedom. While the distribution equation is meant to be formulated for integers, you can also use real values.

• p is a real probability, 0 ≤ p ≤ 1.

• m is an integer, m > 0.