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:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“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)