function poisson03fig2 % Fig. 1.2a Book Illustration for Simple Poisson/Jump Process (3/2007) % RNG Simulation for P(t) = 1:K jumps with sample variation. % Generation is by Poisson Jump Exponentially distributed % jump time increments T(k+1)-T(k), T(k+1) = kth jump time, % T(1) := 0. % clc % clear variables, but must come before globals, % else clears globals too. fprintf('\nfunction poisson03fig2 OutPut:') nfig = 0; K = 10; KP = 2*K +1; % Include sample of K jumps only. p = zeros(KP,1); kstates = 4; LT = zeros(KP,kstates); % Begin Calculation: for kstate = 1:kstates; % Test Multiple Simulated Sample Paths: LT(1,kstate) = 0; p(1) = 0; % Set initial scaled jump time % and jump count. rand('state',kstate); % Set initial state for repeatability % or path change. DTe = -log(rand(K,1)); % Generate random vector of % K exponential variates. for k = 1:K % Simulated sample scaled jump times % LT(k+1) = lambda*T(k+1): LT(2*k,kstate) = LT(2*k-1,kstate) + DTe(k); LT(2*k+1,kstate) = LT(2*k,kstate); p(2*k) = p(2*k-1); p(2*k+1) = p(2*k-1) + 1; end end % Begin Plot: nfig = nfig + 1; scrsize = get(0,'ScreenSize'); % figure spacing for target screen ss = [5.0,4.0,3.5]; % figure spacing factors fprintf('\n\nFigure(%i): Simulated Jump Sample Paths\n',nfig) figure(nfig) plot(LT(1:KP,1),p,'k-',LT(1:KP,2),p,'k:',LT(1:KP,3),p,'k-.' ... ,LT(1:KP,4),p,'k--','LineWidth',2); title('Simulated Simple Jump Sample Paths'... ,'FontWeight','Bold','Fontsize',44); ylabel('P(t), Poisson State'... ,'FontWeight','Bold','Fontsize',44); xlabel('\lambda t, Scaled Time'... ,'FontWeight','Bold','Fontsize',44); hlegend=legend('Sample 1','Sample 2','Sample 3','Sample 4'... ,'Location','Southeast'); set(hlegend,'Fontsize',36,'FontWeight','Bold'); set(gca,'Fontsize',36,'FontWeight','Bold','linewidth',3); set(gcf,'Color','White','Position' ... ,[scrsize(3)/ss(nfig) 60 scrsize(3)*0.60 scrsize(4)*0.80]); %[l,b,w,h] % End Code