随机过程：【1】基于MATLAB对泊松过程的仿真与数字特征的验证.zip

function [Pearson3,Pearson4,Pearson5]=PoissonPlus(result,time,average,lambda) % 此函数用来完成拓展任务，进一步验证余下的三个数字特征 number = size(result,2); %列数 % 均方值的计算，基于定义 result2 = result.^2; MeanSquare = mean(result2(1:number,:)); %计算定义值 MeanSquare_ideal = lambda.*time + (lambda^2).*(time.^2); %计算理论值 figure4 = figure; axes3 = axes('Parent',figure4); hold(axes3,'on'); plot(time,MeanSquare_ideal); plot(time,MeanSquare); ylabel({'数值'}); xlabel({'时间t'}); title({'泊松过程样本均方值与理论值对比图'}); legend('理论值','样本均方值函数'); legend1 = legend(axes3,'show'); set(legend1,... 'Position',[0.177395983388902 0.705548654244307 0.17127696712065 0.178743961352668]); % 自相关函数值的计算，基于定义 % 取t1 = 50 t2 在0-100之间变化，分别计算定义值和理论值 t1 = 50; JI = result(:,t1).*result; selfcorrelation = mean(JI(1:number,:));%计算定义值 t2 = 0:number-1; selfcorrelation_ideal = lambda.*min(t1,t2) + lambda.^2*t1*t2; %计算理论值 figure5 = figure; axes3 = axes('Parent',figure5); hold(axes3,'on'); plot(time,selfcorrelation_ideal); plot(time,selfcorrelation); ylabel({'数值'}); xlabel({'时间t'}); title({'泊松过程样本自相关函数值与理论值对比图'}); legend('理论值','样本自相关函数'); legend1 = legend(axes3,'show'); set(legend1,... 'Position',[0.177395983388902 0.705548654244307 0.17127696712065 0.178743961352668]); % 自协方差函数值的计算，基于定义 % 取t1 = 50 t2 在0-100之间变化，分别计算定义值和理论值 t1 = 50; part1 = (result(:,t1)-average(:,t1)); for t2 = 1:number part2(:,t2) = result(:,t2)-average(:,t2); end autocovariance = mean(part1.*part2); %计算定义值 t2 = 0:number-1; autocovariance_ideal = lambda.*min(t1,t2); %计算理论值 figure6 = figure; axes3 = axes('Parent',figure6); hold(axes3,'on'); plot(time,autocovariance_ideal); plot(time,autocovariance); ylabel({'数值'}); xlabel({'时间t'}); title({'泊松过程样本自协方差函数值与理论值对比图'}); legend('理论值','样本自协方差函数'); legend1 = legend(axes3,'show'); set(legend1,... 'Position',[0.177395983388902 0.705548654244307 0.17127696712065 0.178743961352668]); Pearson3 = corrcoef(MeanSquare,MeanSquare_ideal); Pearson4 = corrcoef(selfcorrelation,selfcorrelation_ideal); Pearson5 = corrcoef(autocovariance,autocovariance_ideal); end