Improving forecasting by learning quantile functions

The quantile function is a mathematical function that takes a quantile (a percentage of a distribution, from 0 to 1) as input and outputs the value of a variable. It can answer questions like, "If I want to guarantee that 95% of my customers receive their orders within 24 hours, how much inventory do I need to keep on hand?" As such, the quantile function is commonly used in the context of forecasting questions. In practical cases, however, we rarely have a tidy formula for computing the quantile function. Instead, statisticians usually use regression analysis to approximate it for a single quantile level at a time.