Understanding the following line of code regarding Gaussian distribution.

2 次查看（过去 30 天）
charu shree
charu shree 2023-8-3
编辑： dpb 2023-8-3
Hello all, I am trying to plot PDF of Gaussian distribution and for that I came across the following code:
In this code, I understand every line except the one which is commented as "Not understood".
I also observed that if we omit this sentence then also code works properly.
Any help in this regard will be highly appreciated.
clc;
clear all;
close all;
% Number of samples
num_samples = 1000;
% Generate random samples from Gaussian distribution
mu_gaussian = 0; % Mean
sigma_gaussian = 1; % Standard deviation
samples_gaussian = mu_gaussian + sigma_gaussian * randn(num_samples, 1); % Not understood
x = linspace(-5, 5, 1000);
pdf_gaussian = (1 / (sigma_gaussian * sqrt(2*pi))) * exp(-(x - mu_gaussian).^2 / (2 * sigma_gaussian^2));
cdf_gaussian = 0.5 * (1 + erf((x - mu_gaussian) / (sigma_gaussian * sqrt(2))));
% Plotting PDFs
figure;
subplot(3, 1, 1);
plot(x, pdf_gaussian, 'b', 'LineWidth', 2);
title('Gaussian Distribution (PDF)');
xlabel('x');
ylabel('Probability Density');

请先登录，再回答此问题。

采纳的回答

Sam Chak
Sam Chak 2023-8-3
Ran in:
Hi @charu shree
This variable samples_gaussian is unused in plotting the pdf and cdf. The code runs without error.
% Number of samples
num_samples = 1000;
% Generate random samples from Gaussian distribution
mu_gaussian = 0; % Mean
sigma_gaussian = 1; % Standard deviation
samples_gaussian = mu_gaussian + sigma_gaussian*randn(num_samples, 1); % Not understood
x = linspace(-5, 5, 1000);
pdf_gaussian = (1/(sigma_gaussian*sqrt(2*pi)))*exp(- (x - mu_gaussian).^2/(2*sigma_gaussian^2));
cdf_gaussian = 0.5*(1 + erf((x - mu_gaussian)/(sigma_gaussian*sqrt(2))));
% Plotting
figure;
subplot(2, 1, 1);
plot(x, pdf_gaussian, 'b', 'LineWidth', 2); grid on
xlabel('x');
ylabel('PDF');
title('Probability Density');
subplot(2, 1, 2);
plot(x, cdf_gaussian, 'b', 'LineWidth', 2); grid on
xlabel('x');
ylabel('CDF');
title('Cumulative Density')
  6 个评论
显示 4更早的评论
Sam Chak
Sam Chak 2023-8-3
Ran in:
Hi @charu shree
The "Not understood" line is actually applying a linear transformation to the random variable.
For more info:
https://stattrek.com/random-variable/transformation
https://bookdown.org/kevin_davisross/probsim-book/linear-rescaling.html
https://proofwiki.org/wiki/Expectation_of_Linear_Transformation_of_Random_Variable
You can visualize the generated random samples in this script:
% Number of samples
num_samples = 1000;
x = linspace(-5, 5, num_samples);
% Normal Distribution with Specific Mean and Variance
desired_mu = 0; % Mean
desired_sigma = 1; % Standard deviation
desired_pdf = (1/(desired_sigma*sqrt(2*pi)))*exp(- (x - desired_mu).^2/(2*desired_sigma^2));
plot(x, desired_pdf, 'LineWidth', 2); hold on
% Generate random samples according to the Linear Transformation of Random Variable
for j = 1:5
norm_samples = desired_mu + desired_sigma*randn(num_samples, 1);
actual_mu(j) = mean(norm_samples);
actual_sigma(j) = std(norm_samples);
pdf_gaussian = (1/(actual_sigma(j)*sqrt(2*pi)))*exp(- (x - actual_mu(j)).^2/(2*actual_sigma(j)^2));
plot(x, pdf_gaussian, '--')
hold on
end
grid on
xlabel('x');
ylabel('PDF');
title('Probability Density');

请先登录，再进行评论。

更多回答（1 个）

dpb
dpb 2023-8-3
编辑：dpb 2023-8-3
It does precisely what the comment ahead of it says it does -- generates a set of psuedo-random normally distributed values with mean mu_gaussian, std deviation sigma_gaussian. Since those are set to 0,1 in the given code, it's the same as what randn returns, but this lets one change the location and dispersion generally.
The code does the same thing whether it is/is not there because while the array was generated, it's never used for anything in the given code; the editor will point that out for you...unless it is used later, of course, but in that case then you would discover that if you were to comment it out and the code tried to reference it. So, one presumes it was "just one of those things" that the original coder had an idea of using/needing a sampled array and then changed mind/direction and never removed the superfluous definition. Or, maybe they never got done...we have no way to know.

类别

在 Help Center 和 File Exchange 中查找有关 Exploration and Visualization 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by