Algorithm 1. Weighted quantile Regression Forest algorithm pseudocode.

input: Number of Trees ($m$), random subset of the features ($mtry$), training dataset ($\mathit{D}$), probability $\alpha$ for quantile estimation

output: weighted quantile Regression Forests ($\mathit{w}\mathit{q}\mathit{R}\mathit{F}$)

1:   $\mathit{w}\mathit{q}\mathit{R}\mathit{F}$ is empty

2:   for each $k$ = 1 to $m$ do

3:     ${\mathit{D}}_k$ = Bootstrap Sample ($\mathit{D}$)

4:     $\mathit{D}{\mathit{T}}_k$ = Random Decision Tree (${\mathit{D}}_k$, $mtry$)

5:     $\mathit{w}\mathit{q}\mathit{R}\mathit{F}$ = $\mathit{w}\mathit{q}\mathit{R}\mathit{F}{\displaystyle \cup }\mathit{D}{\mathit{T}}_k$

6:   end

7:   for each $i$= 1 to $n$ do

8:     Compute $w_i^{obs}$ using Formula (13)

9:   end

10:   for each $k$ = 1 to $m$ do

11:     Compute $wRMS{E}_k$ using Formula (12)

12:   end

13:   for each $k$ = 1 to $m$ do

14:     Compute $w_k$ using Formula (14)

15:   end

16:   Compute final prediction ${\widehat{Q}}_{\alpha }^{weighted}\left(Y|\mathit{X}=\mathit{x}\right)$ using Formula (11)

17:   return $\mathit{w}\mathit{q}\mathit{R}\mathit{F}$