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Difference between revisions of "Percentile"

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One of the numerical characteristics of a [[Probability distribution|probability distribution]]; it is a particular case of a [[Quantile|quantile]]. The <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720201.png" />-th percentile is defined as the quantile <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720202.png" /> corresponding to the value of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720203.png" /> equal to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720204.png" />, for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720205.png" />. For a continuous strictly-monotone distribution function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720206.png" />, the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720207.png" />-th percentile is the solution to
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One of the numerical characteristics of a [[Probability distribution|probability distribution]]; it is a particular case of a [[Quantile|quantile]]. The $j$-th percentile is defined as the quantile $K_p$ corresponding to the value of $p$ equal to $j/100$, for $j=0,\ldots,99$. For a continuous strictly-monotone distribution function $F(x)$, the $j$-th percentile is the solution to
  
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720208.png" /></td> </tr></table>
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$$F(x)=\frac{j}{100},$$
  
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<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072020/p0720209.png" />. In mathematical statistics, the set of percentiles gives a good picture of the distribution. Percentiles are also called centiles or procentiles.
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$j=0,\ldots,99$. In mathematical statistics, the set of percentiles gives a good picture of the distribution. Percentiles are also called centiles or procentiles.
  
  

Latest revision as of 09:00, 12 April 2014

One of the numerical characteristics of a probability distribution; it is a particular case of a quantile. The $j$-th percentile is defined as the quantile $K_p$ corresponding to the value of $p$ equal to $j/100$, for $j=0,\ldots,99$. For a continuous strictly-monotone distribution function $F(x)$, the $j$-th percentile is the solution to

$$F(x)=\frac{j}{100},$$

$j=0,\ldots,99$. In mathematical statistics, the set of percentiles gives a good picture of the distribution. Percentiles are also called centiles or procentiles.


Comments

References

[a1] Ph.H. Dubois, "An introduction to psychological statistics" , Harper & Row (1965) pp. 412ff
How to Cite This Entry:
Percentile. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Percentile&oldid=31604
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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