Probability Distributions

In order to input your own data you will need to open in Desmos

how to use

takes data input in the for of a list of values

can calculate normal, triangular, and rectangular prediction models based on the data provided.

Equations $$f_{unc}\ =\ \left[f_{n}\left(x\right),f_{r}\left(x\right),f_{t}\left(x\right)\right]$$

Normal Distribution $$f_{n}\left(x\right)=\frac{1}{s_{d}\cdot\left(2\pi\right)^{0.5}}e^{-\frac{1}{2}\left(\frac{x-m}{s_{d}}\right)^{2}}$$

Rectangular Distribution $$f_{r}\left(x\right)={\min\left(d\right)<x<\max\left(d\right):\frac{1}{\left(\max\left(d\right)-\min\left(d\right)\right)},}$$

Triangular Distribution $$f_{t}\left(x\right)={\min\left(d\right)<x<t_{c}:\frac{2\left(x-\min\left(d\right)\right)}{\left(\max\left(d\right)-\min\left(d\right)\right)\left(t_{c}-\min\left(d\right)\right)},t_{c}<x<\max\left(d\right):\frac{2\left(\max\left(d\right)-x\right)}{\left(\max\left(d\right)-\min\left(d\right)\right)\left(\max\left(d\right)-t_{c}\right)},}$$

The best distribution is calculated using this function $$m_{atch}=\left[\sum_{w=\frac{r_{g}}{100}}^{100}\left(f_{p}\left(w,w+\frac{r_{g}}{100},i_{12}\right)-\frac{\operatorname{count}\left(d\left[w<d<w+\frac{r_{g}}{10}\right]\right)}{\operatorname{count}\left(d\right)}\right)^{2}\ \operatorname{for}\ i_{12}=\left[1...f_{unc}.\operatorname{length}\right]\right]$$

click find best distro to find the best model to fit your data