I have a normal distribution N(1,0) and have to split it in n-pieces where the area under the curve is equal i.e. 1/n
Now I need to find the specific points/values where this happen.
f(1 .. n) =
How do I do that ? If you can provide pseudo code it will be good too i.e. i need to make it python code.
PS> I'm trying to implement this :
https://www.cs.ucr.edu/~eamonn/SAX.pdf
page 5 : Discretization
I hope I'm describing the problem OK! I'm abit confused by why they need table, instead of just list of numbers i.e. points/values.
Let $\Phi^{-1}$ be the quantile function of the standard normal distribution, then the points $$\Phi^{-1}(0),\Phi^{-1}(\frac1n), \Phi^{-1}(\frac2n),\dots\Phi^{-1}(\frac{n-1}{n}),\Phi^{-1}(1),$$ where $\Phi^{-1}(0)=-\infty$ and $\Phi^{-1}(1)=\infty$, will divide the real line into intervals, which each have probability $\frac{1}{n}$ with respect to a $N(0,1)$ distribution.
Let's verify this. Let $Z\sim N(0,1)$, then \begin{align*} P(\Phi^{-1}(\frac{k}{n}) \leq Z \leq \Phi^{-1}(\frac{k+1}{n})) &= \Phi(\Phi^{-1}(\frac{k+1}{n}))-\Phi(\Phi^{-1}(\frac{k}{n})) \\ &= \frac{k+1}{n}-\frac{k}{n} \\ &= \frac{1}{n} \end{align*} The quantile function $\Phi^{-1}$ can be computed in Python with the norm.ppf() function from the scipy.stats module https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html .