Quantile transformation with SAS using z-scores?

Question

Given is a value quantile_x (say 42 Euro) which corresponds to the x-quantile (say 99%) of a (non-normalized) Gaussian distribution. I am now interested of the value quantile_y corresponding to the y-quantile (say 95%).

I would love to simply write

proc sql;
   create table want as
   select quantile_x
         ,%transform(quantile_x,x,y) as quantile_y
   from have;
quit;

For the given example, %transform() should actually simply perform the following product

quantile_y = quantile_x * 1.645 / 2.326

The numbers are the z-scores for 97% quantile and the 99% quantile, respectively. Somehow, I failed to figure out, how I can obtain these two numbers using SAS.

Edit: Reading SAS docu on probnorm it looks like I am after its inverse function since probnorm(1.96)=0.9750021049.

References

• SAS-Blog: Four essential functions for statistical programmers
• Philippe Jorion's Introduction to Value-at-Risk (VaR)
• Wolframalpha z-score for 0.99
• https://communities.sas.com/t5/SAS-Procedures/Calculate-Z-Score/td-p/501718

Answer 1

Use the quantile() function.

data have;
  input x y actual;
  z_x = quantile('NORMAL',x);
  z_y = quantile('NORMAL',y);
  adjusted = actual * z_y / z_x;
cards;
 .99 .95 2.32635
 .99 .95 42
;

Results:

Obs      x       y      actual      z_x        z_y      adjusted

 1     0.99    0.95     2.3264    2.32635    1.64485      1.6449
 2     0.99    0.95    42.0000    2.32635    1.64485     29.6963