I have a dependent variable and variable Age as the independent variable. I want to apply the quantile regression for 0.025 and 0.95 quantiles and I have this shape[![enter image description here][1]][1]

So I decided to use the power transformation method for the dependent variable and this is the new shape
[![enter image description here][2]][2]
Any advice how can I apply quantile regression for this variable? I calculated the quantile curve and you can see them in the following plot. 
[![enter image description here][3]][3]


  [1]: https://i.sstatic.net/gmw0s.png
  [2]: https://i.sstatic.net/5ezqV.png
  [3]: https://i.sstatic.net/BBGGA.png