Re-centering a t-skew distribution

Hi I have a t-skew distribution, but I need to recenter it so as to have a new fixed mode, and ideally a fixed tail (i.e) 5th percentile. Is that possible ?

For instance, in the attached file - I would prefer the mode to be 1.822, and the 5th percentile value to be around -4.4.

Is that too much to expect ?

Answer 1

[Jeff Miller]

I take it you want to find the values a,b for a linear transformation such that

newScores = a + b*oldScores;

Presumably you can also supply the values oldMode and old5thpctile. Then you just have to solve for a,b:

1.822 = a + b*oldMode;  % put the new mode at 1.822
-4.4 = a + b*old5thpctile;  % put the new 5th pctile at -4.4

If you don't want to do the algebra yourself, try this:

syms a b oldMode old5thpctile
modeeqn = 1.822 == a + b*oldMode;
pctileeqn = -4.4 == a + b*old5thpctile;
[sola, solb] = solve([modeeqn, pctileeqn],a,b)

which gives

sola =
-(2200*oldMode + 911*old5thpctile)/(500*(oldMode - old5thpctile))
solb =
3111/(500*(oldMode - old5thpctile))