Chapter 3: the squaring transform for conversion between variance and sd

The squaring transform [i.e., f(t)=t^2] changes a distribution in standard deviation units to one in variance units. Starting with a uniform distribution over standard deviation, we arrive at the (approximate sampled) transformed distribution via the Matlab commands:

SDs=.005:.01:1-.005; %create vector of SD values

pSD=ones(size(SDs)); %uniform probability dist over SD values

vTX=@(x) x.^2; %linking function for variance units

PvTX=pTX(SDs,pSD,vTX); %compute squaring transform of sd probabilities

Similarly, we can compute a transformed distribution over SD starting from a distribution over possible variance values:

Vs=.005:.01:1; %create vector of var values

pV=ones(size(Vs)); %uniform probability dist over var values

sdTX=@(x) sqrt(x); %linking function for SD units

PsdTX=pTX(Vs,pV,sdTX); %compute sqrt transform of var probabilities