# Fitting a curve on a log log plot

## Learning goals

1. Know the axioms for a distance measure and how they relate to norms.
2. Know at least two distance measures on functions spaces.
3. Understand why changing to the CDF makes sense when looking at distance between functions.
4. Understand the principle of the Kolomogorov-Smirnov test for fitting curves

## Quiz

1

supose we have ${\displaystyle f=sin(x)}$. What is the value of${\displaystyle ||f(x)||_{\infty }}$

 -1 0 1 ${\displaystyle \pi }$ ${\displaystyle 2\pi }$

2

supose we have ${\displaystyle f:[0,6]\longrightarrow \mathbb {R} }$ with ${\displaystyle f(x)=x}$. What is the value of${\displaystyle ||f(x)||_{\infty }}$

 x 1 6 12 18

3

supose we have ${\displaystyle f:[0,6]\longrightarrow \mathbb {R} }$ with ${\displaystyle f(x)=x}$. What is the value of${\displaystyle ||f(x)||_{1}}$

 x 1 6 12 18

4

What is true about the Kolmogorov-Smirnov Test

 It is often used to fit a curve It must be used to fit a curve it uses the uniform norm of the curve and observed data it uses the uniform norm on the CDF of the curve and the CDF of the observed data it uses the L1-norm on the CDF of the curve and the CDF of the observed data