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In probability and statistics, the quantile function specifies, for a given probability in the probability distribution of a random variable, the value at which the probability of the random variable being less than or equal to this value is equal to the given probability. It is also called the percent point function or inverse cumulative distribution function. ==Definition== With reference to a continuous and strictly monotonic distribution function, for example the cumulative distribution function of a random variable ''X'', the quantile function ''Q'' returns a threshold value ''x'' below which random draws from the given c.d.f would fall ''p'' percent of the time. In terms of the distribution function ''F'', the quantile function ''Q'' returns the value ''x'' such that : Another way to express the quantile function is : for a probability 0 < ''p'' < 1. Here we capture the fact that the quantile function returns the minimum value of ''x'' from amongst all those values whose c.d.f value exceeds ''p'', which is equivalent to the previous probability statement. If the function ''F'' is continuous, then the infimum function can be replaced by the minimum function and : Note: if the probability distribution is discrete rather than continuous then there may be gaps between values in the domain of its cdf, while if the cdf is only weakly monotonic there may be "flat spots" in its range. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「quantile function」の詳細全文を読む スポンサード リンク
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