Quantile Function - Definition

Definition

Assuming a continuous and strictly monotonic distribution function, the quantile function returns the value below which random draws from the given distribution would fall, p×100 percent of the time. That is, it returns the value of x such that

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. In either case, the quantile function is

for a probability 0 < p < 1, and the quantile function returns the minimum value of x for which the previous probability statement holds.

Read more about this topic:  Quantile Function

Famous quotes containing the word definition:

    Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.
    Walter Pater (1839–1894)

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.
    Ralph Waldo Emerson (1803–1882)