Quantile

Explained:

percentile

quantile

quartile


Consider a random variable X. A 0.75-quantile of X is any value x such that Pr(X ≤ x) = .75. This is illustrated with a hypothetical probability density function for X in Exhibit 1.

Example: 0.75-Quantile
Exhibit 1

A 0.75-quantile of X is any value x such that
Pr(X ≤ x) = .75.
   

More generally, a q-quantile of a random variable X is any value x such that Pr(X ≤ x) = q. If a random variable is not continuous, or if it has zero probability density on some interval, quantiles may not be unique or may not exist.

Certain quantiles have special names. The 0.25-, 0.50-, and 0.75-quantiles are called the first, second and third quartiles. The 0.01-, 0.02-, 0.03-, ... , 0.98-, 0.99-quantiles are called the first, second, third, ... , ninety-eighth, and ninety-ninth percentiles.

Related Internal Links

Cornish-Fisher expansion A formula for approximating quintiles of a random variable based only on its first few cumulants.

expected value A parameter describing the "center of gravity" of a distribution.

kurtosis A parameter describing the peakedness and tails of a distribution.

normal distribution A continuous probability distribution whose probability density function has a "bell" shape.

skewness A parameter that describes the lack of symmetry of a distribution.

standard deviation A parameter describing the dispersion of a distribution.

uniform distribution A continuous probability distribution that has constant probability on a finite interval.

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copyright © Glyn A. Holton, 1996, 2004

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