Generate Independent Identically and Lognormally Distributed Random Variables

Question

Ghifari Adam Faza 2019-7-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/472741-generate-independent-identically-and-lognormally-distributed-random-variables

评论： Ghifari Adam Faza 2019-7-22

I am trying to create a script for simple reliability analysis. It works fine with other test cases. But, whenever I tried to solve the following test case the result is incorrect. I suppose that the error is in the sampling process.

Where

are the independent dentically and lognormally distributed random variables with unit means and standard deviations

. The value of n is chosen to be 40.

Later, the function will be applied on

points and then the Probability of failure is calculated by using:

[3]

According to the references the value of Pf should be around

. Meanwhile, my Pf is 1.

References:

Bourinet, J.-M., Deheeger, F., & Lemaire, M. (2011). Assessing small failure probabilities by combined subset simulation and Support Vector Machines. Structural Safety, 33(6), 343–353. doi:10.1016/j.strusafe.2011.06.001
Xu, J., & Zhu, S. (2019). An efficient approach for high-dimensional structural reliability analysis. Mechanical Systems and Signal Processing, 122, 152–170.
Echard, B., Gayton, N., & Lemaire, M. (2011). AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation. Structural Safety, 33(2), 145–154.

Here's my script:

clear;
nvar = 40;
sigma = 0.2;
nmc = 3e5;
mu = 1;
init_samp = lognrnd(mu,sigma,nmc,nvar);
% Evaluation func
gx = (nvar + 3*sigma*sqrt(nvar)) - sum(init_samp,2);
%count negative
nneg = length(find(gx < 0));
Pf = nneg/nmc;
disp(Pf)
x = -2:.1:10;
[f,xi] = ecdf(gx);
semilogy(xi,f,'LineWidth',2)
ylim([1E-4,1])
grid on;

Thank you very much!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Torsten 2019-7-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/472741-generate-independent-identically-and-lognormally-distributed-random-variables#answer_384174

Note that mu and sigma you supply for "lognrnd" are not mean and standard deviation of the underlying lognormal distribution, but the distribution parameters mu and sigma.

See the first example under

https://de.mathworks.com/help/stats/lognrnd.html