High Quality Content by WIKIPEDIA articles! In probability theory, a quantile function of a probability distribution is the inverse F ?1 of its cumulative distribution function (cdf) F. Assuming a continuous and strictly monotonic distribution function, scriptstyle Fcolon R to (0,1), the quantile function returns the value below which random draws from the given distribution would fall, px100 percent of the time. Quantile functions are used in both statistical applications and Monte-Carlo methods. For statistical applications, users need to know key percentage points of a given distribution. For example, they require the median and 25% and 75% quartiles as in the example above or 5%, 95%, 2.5%, 97.5% levels for other applications such as assessing the statistical significance of an observation whose distribution is known; see the quantile entry. Statistical applications of quantile functions are discussed extensively by Gilchrist (2000).

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