A.3 Quantile functions
Suppose that F : (a, b) → ℝ is an increasing function which is not necessarily strictly increasing. Let
Definition A.18. A function q : (c, d) → (a, b) is called an inverse function for F if
The functions
are called the left- and right-continuous inverse functions.
◊
The following lemma explains the reason for calling q− and q+ the left- and right-continuous inverse functions of F.
Lemma A.19. A function q : (c, d) → (a, ...
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