Using a transition matrix as input to a cummulative matrix

**Walter12** · 10-25-2012, 11:55 AM

Hi,

I have a cummulative matrix (based on the help from a previous thread) which I use for deciding the probability of a program switching between values, but I'd like to use a simpler transition matrix as input (as people understand that a bit better).

Currently I have a matrix that looks like:

       ----A---- -B-- -C-- -D--
   1   From \ To  r1   r2   r3 
   2      r1     0%   65%  80%
   3      r2     0%   0%    60%
   4      r3     0%  20%   70%

Which I use to determine the probability of switching between r1, r2 and r3.

I'd like a user to be able to input three values

Probability when in Regime 1 of staying in Regime 1
Probability when in Regime 2 of staying in Regime 2
Probability when in Regime 3 of staying in Regime 3

And to calculate the corresponding probabilities as input to my cumulative matrix. Trouble is, I'm stuck on the math of how to do this.

**protonLeah** · 10-26-2012, 02:18 AM

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**Walter12** · 10-26-2012, 04:19 AM

So my input matrix should look like:

      ----A---- -B-- -C-- -D--
   1   From \ To  r1   r2   r3 
   2      r1     70%   25%  5%
   3      r2     10%   80%  10%
   4      r3     5%  25%   70%

Which would feed into my cummulative matrix to look like:

      ----A---- -B-- -C-- -D--
   1   From \ To  r1   r2   r3 
   2      r1     0%   70%  95%
   3      r2     0%   10%  90%
   4      r3     0%   5%   30%