本文详细介绍了Copula函数的绘制及在可靠度分析中的应用
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- 各种类型Copula函数绘图
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- 完整代码
- 例题1
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- 完整代码
- 例题2
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- 完整代码
各种类型Copula函数绘图
完整代码
clear
clc
y_gaussian = copularnd('gaussian', 0.9, 1000);
y_t = copularnd('t', 0.91, 17.53,1000);
y_Gumbel = copularnd('Gumbel', 3.22,1000);
y_Clayton = copularnd('Clayton', 3.06,1000);
y_Frank = copularnd('Frank', 12.04,1000);
subplot(2,3,1.4)
plot(y_gaussian(:,1), y_gaussian(:,2),'.')
xlabel('u')
ylabel('v')
title('Gaussian(\theta = 0.90)')
set(gca,'FontName','Times New Roman','FontSize',14);
subplot(2,3,2.6)
plot(y_t(:,1), y_t(:,2),'.')
xlabel('u')
ylabel('v')
title('t(\theta = 0.90, \nu =17.53)')
set(gca,'FontName','Times New Roman','FontSize',14);
subplot(2,3,4)
plot(y_Gumbel(:,1), y_Gumbel(:,2),'.')
xlabel('u')
ylabel('v')
title('Gumbel(\theta = 3.22)')
set(gca,'FontName','Times New Roman','FontSize',14);
subplot(2,3,5)
plot(y_Clayton(:,1), y_Clayton(:,2),'.')
xlabel('u')
ylabel('v')
title('Clayton(\theta = 3.06)')
set(gca,'FontName','Times New Roman','FontSize',14);
subplot(2,3,6)
plot(y_Frank(:,1), y_Frank(:,2),'.')
xlabel('u')
ylabel('v')
title('Frank(\theta = 12.04)')
set(gca,'FontName','Times New Roman','FontSize',14);
例题1
设结构的极限状态方程为 Z = X 1 − X 2 − X 3 = 0 Z = X_1 - X_2 -X_3 = 0 Z=X1−X2−X3=0。其中， X 1 , X 2 , X 3 X_1, X_2, X_3 X1,X2,X3 均服 从正态分布,其均值和标准差分别为 μ X 1 = 21.6788 \mu_{X_1} = 21.6788 μX1=21.6788 , σ X 1 = 2.6014 \sigma_{X_1} = 2.6014 σX1=2.6014； μ X 2 = 10.4 \mu_{X_2} = 10.4 μX2=
