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:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)