Esempio: curtosi e dissimmetria

Funzioni > Statistica > Statistiche descrittive > Esempio: curtosi e dissimmetria

Utilizzare le funzioni kurt e skew per confrontare la forma di una distribuzione di Weibull e di una distribuzione normale.

1. Definire le distribuzioni indicate di seguito e tracciarne il grafico.

Fare clic per copiare questa espressione

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2. Confrontare il picco delle distribuzioni calcolando la curtosi delle distribuzioni.

Le barre dell'istogramma indicano la leggera deviazione da zero della curtosi della distribuzione normale. La curtosi della distribuzione di Weibull indica che tale distribuzione presenta un leggero picco in confronto alla distribuzione normale.

È possibile stimare la curtosi della popolazione tramite il coefficiente di curtosi campione indicato di seguito.

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    <define xmlns="http://schemas.mathsoft.com/math50">
      <function>
        <id label="None">kurtosis</id>
        <boundVars>
          <id label="None">v</id>
        </boundVars>
      </function>
      <apply>
        <minus />
        <apply>
          <div />
          <apply>
            <mult />
            <apply>
              <mult />
              <apply>
                <id>rows</id>
                <id>v</id>
              </apply>
              <parens>
                <apply>
                  <plus />
                  <apply>
                    <id>rows</id>
                    <id>v</id>
                  </apply>
                  <real>1</real>
                </apply>
              </parens>
            </apply>
            <apply>
              <summation />
              <lambda>
                <boundVars>
                  <placeholder />
                </boundVars>
                <apply>
                  <pow />
                  <parens>
                    <apply>
                      <minus />
                      <id>v</id>
                      <apply>
                        <id>mean</id>
                        <id>v</id>
                      </apply>
                    </apply>
                  </parens>
                  <real>4</real>
                </apply>
              </lambda>
              <upperBound>
                <placeholder />
              </upperBound>
            </apply>
          </apply>
          <apply>
            <mult />
            <apply>
              <mult />
              <apply>
                <mult />
                <parens>
                  <apply>
                    <minus />
                    <apply>
                      <id>rows</id>
                      <id>v</id>
                    </apply>
                    <real>1</real>
                  </apply>
                </parens>
                <parens>
                  <apply>
                    <minus />
                    <apply>
                      <id>rows</id>
                      <id>v</id>
                    </apply>
                    <real>2</real>
                  </apply>
                </parens>
              </apply>
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <id>rows</id>
                    <id>v</id>
                  </apply>
                  <real>3</real>
                </apply>
              </parens>
            </apply>
            <apply>
              <pow />
              <apply>
                <id>Stdev</id>
                <id>v</id>
              </apply>
              <real>4</real>
            </apply>
          </apply>
        </apply>
        <apply>
          <div />
          <apply>
            <mult />
            <real>3</real>
            <apply>
              <pow />
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <id>rows</id>
                    <id>v</id>
                  </apply>
                  <real>1</real>
                </apply>
              </parens>
              <real>2</real>
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          </apply>
          <apply>
            <mult />
            <parens>
              <apply>
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                <apply>
                  <id>rows</id>
                  <id>v</id>
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                <real>2</real>
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            </parens>
            <parens>
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                  <id>rows</id>
                  <id>v</id>
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                <real>3</real>
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3. Confrontare l'inclinazione delle distribuzioni.

La distribuzione di Weibull si riduce a destra.

È possibile stimare la dissimmetria in una popolazione tramite il coefficiente di dissimmetria campione indicato di seguito.

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        <id label="None">skewness</id>
        <boundVars>
          <id label="None">v</id>
        </boundVars>
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        <apply>
          <mult />
          <apply>
            <id>rows</id>
            <id>v</id>
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          <apply>
            <summation />
            <lambda>
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                <placeholder />
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              <apply>
                <pow />
                <parens>
                  <apply>
                    <minus />
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                    <apply>
                      <id>mean</id>
                      <id>v</id>
                    </apply>
                  </apply>
                </parens>
                <real>3</real>
              </apply>
            </lambda>
            <upperBound>
              <placeholder />
            </upperBound>
          </apply>
        </apply>
        <apply>
          <mult />
          <apply>
            <mult />
            <parens>
              <apply>
                <minus />
                <apply>
                  <id>rows</id>
                  <id>v</id>
                </apply>
                <real>1</real>
              </apply>
            </parens>
            <parens>
              <apply>
                <minus />
                <apply>
                  <id>rows</id>
                  <id>v</id>
                </apply>
                <real>2</real>
              </apply>
            </parens>
          </apply>
          <apply>
            <pow />
            <apply>
              <id>Stdev</id>
              <id>v</id>
            </apply>
            <real>3</real>
          </apply>
        </apply>
      </apply>
    </define>
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