I have a set of points whose shape is as below
Its set of $x$ and $y$ points is as follows:
$x=[0.14741,0.180288,0.195,0.245342,0.25614,0.289377,0.315789,0.357143,0.431034,1.785714,2,2.323529,2.586207,3,3.894737,4.923077]$
$y=[0.211718,0.408906,0.507768,0.832,0.903626,1.092787,1.368377,1.750082,2.593839,1.72126,1.653633,1.567115,1.502963,1.419437,1.279676,1.153634]$
Can anyone fit a distribution with at least three degrees of freedom to these points? Do I need the name of the distribution and its coefficients? Does anyone have an idea of writing code with Python to get the coefficients and type of distribution? This chart is the most similar to the chi-square and Double Exponential charts.