Calculating quantile of distribution function

Question

I'm having a problem with a statitics example.

The calculation for my quantile is not difficult. But I'm wondering which part of my function I need to use.

Let's say my distribution function is like:

$$ F(x)=\begin{cases} \frac {1}{4} x - \frac {3}{2} & \mbox{for } 6 \le x \le 8 \\ \frac {5}{2} - \frac {1}{4} x & \mbox{for } 8 < x \le 10 \\ 0 & \mbox{else} \end{cases} $$

Now. If I need to calculate a Quantile - 0.7 or 0.3 - I know that $ F(x) = 0.3 $, but how do I know which part of my function I need to use?

Answer 1

The only important "transition" from one formula to another occurs at $x=8$. By finding $F(8)$, which turns out to be $1/2$, you discover that if you want, for example, to find out where $F(x)=0.2$, you need to find where $\frac{1}{4}x-3/2=0.2$. If on the other hand you want to find out where $F(x)=0.9$, then since $0.9\gt F(8)=1/2$, you need to find out where $\frac{5}{2}-\frac{1}{4}x=0.9$.

-- André Nicolas