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smctp2stat

PURPOSE ^

Stationary distributions for a switching MCTP.

SYNOPSIS ^

[ro,ro_min,ro_max,Ro_min,Ro_max,QQ] = mctp2stat(P,F)

DESCRIPTION ^

  SMCTP2STAT  Stationary distributions for a switching MCTP. 
  
  CALL: [ro,ro_min,ro_max] = smctp2stat(P,F); 
        [ro,ro_min,ro_max,Ro_min,Ro_max] = smctp2stat(P,F); 
  
  ro     = Stationary distribution of regime process.   [1xr] 
  ro_min = Stationary distr. of minima for subloads. {r}[1xn] 
  ro_max = Stationary distr. of maxima for subloads. {r}[1xn] 
  Ro_min = Stationary distr. of minima for joint MCTP.  [1xnr] 
  Ro_max = Stationary distr. of maxima for joint MCTP.  [1xnr] 
  
  P      = Transition matrix for regime process.        [rxr] 
  F      = Cell array of min-Max and Max-min matrices   {rx2} 
  F{i,1} = min-Max matrix, process i                    [nxn] 
  F{i,2} = Max-min matrix, process i                    [nxn] 
  
  See also  mctp2stat, smctp2joint

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function [ro,ro_min,ro_max,Ro_min,Ro_max,QQ] = mctp2stat(P,F) 
002 % SMCTP2STAT  Stationary distributions for a switching MCTP. 
003 % 
004 % CALL: [ro,ro_min,ro_max] = smctp2stat(P,F); 
005 %       [ro,ro_min,ro_max,Ro_min,Ro_max] = smctp2stat(P,F); 
006 % 
007 % ro     = Stationary distribution of regime process.   [1xr] 
008 % ro_min = Stationary distr. of minima for subloads. {r}[1xn] 
009 % ro_max = Stationary distr. of maxima for subloads. {r}[1xn] 
010 % Ro_min = Stationary distr. of minima for joint MCTP.  [1xnr] 
011 % Ro_max = Stationary distr. of maxima for joint MCTP.  [1xnr] 
012 % 
013 % P      = Transition matrix for regime process.        [rxr] 
014 % F      = Cell array of min-Max and Max-min matrices   {rx2} 
015 % F{i,1} = min-Max matrix, process i                    [nxn] 
016 % F{i,2} = Max-min matrix, process i                    [nxn] 
017 % 
018 % See also  mctp2stat, smctp2joint 
019  
020 % Tested  on Matlab  5.3 
021 % 
022 % History: 
023 % Updated by PJ 18-May-2000 
024 %   updated for WAFO 
025 % Created by PJ (Pär Johannesson) 1999 
026  
027 % Check input arguments 
028  
029 ni = nargin; 
030 no = nargout; 
031 error(nargchk(2,2,ni)); 
032  
033 % Define  
034  
035 r = length(P);   % Number of regime states 
036 n = length(F{1,1});  % Number of levels 
037  
038 % Check that the rowsums of P are equal to 1 
039  
040 P = mat2tmat(P); 
041  
042 % Normalize the rowsums of F{1,1},...,F{r,1} to 1 
043 %  ==>  QQ{1,1},...,QQ{r,1} 
044  
045 for i = 1:r 
046   QQ{i,1} = F{i,1}; 
047   QQ{i,1} = mat2tmat(QQ{i,1},1); 
048 end 
049  
050 % Normalize the rowsums of F{1,2},...,F{r,2} to 1 
051 %  ==>  QQ{1,2},...,QQ{r,2} 
052  
053 for i = 1:r 
054    
055   if isempty(F{i,2})        % Time-reversible 
056     QQ{i,2} = F{i,1}'; 
057   else                   % F{i,2} is given 
058     QQ{i,2} = F{i,2};  
059   end 
060      
061   QQ{i,2} = mat2tmat(QQ{i,2},-1); 
062  
063 end 
064  
065 % Stationary distribution (=ro) for regime process. 
066  
067 ro = mc2stat(P); 
068  
069 % Stationary distribution (=ro) of local minima with transition matrix 
070 % Qt = Q*Qh = "Transition matrix for min-to-min" 
071  
072 for i = 1:r 
073   [ro_min{i},ro_max{i}] = mctp2stat(F(i,:)); 
074 end 
075  
076 [Q,QQ] = smctp2joint(P,F) 
077  
078 [Ro_min,Ro_max] = mctp2stat(Q); 
079  
080  
081

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group


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