Transition Matrix -ve states and sum not 1, or 1 with negative probablities
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I have implemented following equation in Matalb
This equation is for calculating transition Matrix Probabilities (Pi,i+j) of this Markov Chain
The code i have written is as follows, where Nt=2:
for i=0:Nt % sum over all i's
for d=0:Nt %sum over all d's
for d1=0:min(i,d) %sum for all possible d1's
for a=0:d %sum for all a's
%index=sprintf("Index i=%d j=%d i=%d i+j=%d \n",i,d1-a, i,i+d1-a)
for k=a:d
if (i==0 || d1==i)
p=pf;
else
p=pa;
end
A= nchoosek(d,k) * (PSI^k) *( (1-PSI)^(d-k) )* nchoosek(k,a) *(p^a)*(1-p)^(k-a);
if( Nt-i > d-d1)
%A= nchoosek(d,k) * PSI *( (1-PSI)^(d-k) )* nchoosek(k,a) *(p^a)*(1-p)^(k-a);
M=nchoosek(i,d1)* nchoosek(Nt-i,d-d1) *(Pi1^d)* (1-Pi1)^(Nt-d) * A ;
end
%make transition matrix array
%newIndex=sprintf("Index i=%d j=%d i=%d i+j=%d \n",i,d1-a, i,i+d1-a)
%values=sprintf("Index i=%d d=%d d1=%d a=%d ,k=%d j=%d i=%d i+j=%d \n",i,d,d1,a,k,d1-a, i,i+d1-a)
if ( (i+d1-a) > 0 && (i+d1-a <= Nt)) %( (i<=Nt) && (i+d1-a <=Nt) && (i+d1-a >=0) )
% newIndex=sprintf("Index i=%d j=%d i=%d i+j=%d \n",i,d1-a, i,i+d1-a);
TM(i+1,i+d1-a+1)=TM(i+1,i+d1-a+1)+M; % for indexing +1
end
end
end
end
end
end
Following are observations from this equation 1) I get negative index sometimes eg. for i+j i.e. Pi,i+j =P0,-1 we dont have '-1' as state. 2) The transition Matrix sums to 1 for about 75% rows. When i ran this code with Nt=40. i was getting sum of rows=1 for 35 rows only. With Nt=10, first row becomes all 0's and 4 rows have sum equal to '1'. 3) In some cases sum of Rows element =1 when having negative probabilities like 1.234 -0.234 0.0 = 1
Can any expert tell me if i have mistakes in code or else.
Thank you
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