Hello everyone!

I need to justify for my dissertation the problems of false detection of a signal by a normal distribution (Gaussian) and build a graph where I should get a decreasing exponent in the interval for P from 10^-8 to 10^-1, and for alpha squared (alpha^2) from 10 to 100. The sigma dispersion = from 10 to 100. The threshold value of the signal n2 = 1.5, from which the normal value is integrated to infinity to calculate the probability of P.

I wrote the following code:

% Given parameters
sigma2_values ​​​​= linspace (0.1, 0.01, 100); % dispersion values ​​from 0.01 to 1000
n2 = 1.5; % threshold value
P_loznoe = zeros(length(sigma2_values), 1); % Initialize array for P_false

% Calculate P_false for each value of sigma^2 for fixed n2
for j = 1: length(sigma2_values)
sigma2 = sigma2_values(j); % use current value of sigma^2
alpha2 = 1/sigma2; % Calculate alpha^2

% Calculate integral of P(x) from n2 to infinity
integrand = @(x) (1 / (sqrt(2 * pi * sigma2))) .* exp(-((x.^2) / (2 * sigma2)));
P_loznoe(j) = integral(integrand, n2, Inf); % Calculate the integral
end

% Calculate alpha^2 for each sigma^2
alpha2_values ​​= 1 ./sigma2_values; % alpha^2 = 1/sigma^2

% Plot P_false vs. alpha^2
figure;
semilogy(alpha2_values, P_loznoe, ‘r’, ‘LineWidth’, 2); % Logarithmic scale on the Y axis
title(‘False discovery rate vs. alpha^2’);
xlabel(‘alpha^2’);
ylabel(‘P_{false}’);
xlim([10 100]); % Set limits on the X axis
ylim([10^(-8) 10^(-1)]); % Set limits on the Y axis to expand the grid
grid on; % Grid on

But for some reason my graph is not in the specified interval and not in the form of a decreasing exponent, but in the form of a linear decrease.

How can this be fixed?

Thanks in advance!Hello everyone!

I need to justify for my dissertation the problems of false detection of a signal by a normal distribution (Gaussian) and build a graph where I should get a decreasing exponent in the interval for P from 10^-8 to 10^-1, and for alpha squared (alpha^2) from 10 to 100. The sigma dispersion = from 10 to 100. The threshold value of the signal n2 = 1.5, from which the normal value is integrated to infinity to calculate the probability of P.

I wrote the following code:

% Given parameters
sigma2_values ​​​​= linspace (0.1, 0.01, 100); % dispersion values ​​from 0.01 to 1000
n2 = 1.5; % threshold value
P_loznoe = zeros(length(sigma2_values), 1); % Initialize array for P_false

% Calculate P_false for each value of sigma^2 for fixed n2
for j = 1: length(sigma2_values)
sigma2 = sigma2_values(j); % use current value of sigma^2
alpha2 = 1/sigma2; % Calculate alpha^2

% Calculate integral of P(x) from n2 to infinity
integrand = @(x) (1 / (sqrt(2 * pi * sigma2))) .* exp(-((x.^2) / (2 * sigma2)));
P_loznoe(j) = integral(integrand, n2, Inf); % Calculate the integral
end

% Calculate alpha^2 for each sigma^2
alpha2_values ​​= 1 ./sigma2_values; % alpha^2 = 1/sigma^2

% Plot P_false vs. alpha^2
figure;
semilogy(alpha2_values, P_loznoe, ‘r’, ‘LineWidth’, 2); % Logarithmic scale on the Y axis
title(‘False discovery rate vs. alpha^2’);
xlabel(‘alpha^2’);
ylabel(‘P_{false}’);
xlim([10 100]); % Set limits on the X axis
ylim([10^(-8) 10^(-1)]); % Set limits on the Y axis to expand the grid
grid on; % Grid on

But for some reason my graph is not in the specified interval and not in the form of a decreasing exponent, but in the form of a linear decrease.

How can this be fixed?

Thanks in advance! Hello everyone!

I need to justify for my dissertation the problems of false detection of a signal by a normal distribution (Gaussian) and build a graph where I should get a decreasing exponent in the interval for P from 10^-8 to 10^-1, and for alpha squared (alpha^2) from 10 to 100. The sigma dispersion = from 10 to 100. The threshold value of the signal n2 = 1.5, from which the normal value is integrated to infinity to calculate the probability of P.

I wrote the following code:

% Given parameters
sigma2_values ​​​​= linspace (0.1, 0.01, 100); % dispersion values ​​from 0.01 to 1000
n2 = 1.5; % threshold value
P_loznoe = zeros(length(sigma2_values), 1); % Initialize array for P_false

% Calculate P_false for each value of sigma^2 for fixed n2
for j = 1: length(sigma2_values)
sigma2 = sigma2_values(j); % use current value of sigma^2
alpha2 = 1/sigma2; % Calculate alpha^2

% Calculate integral of P(x) from n2 to infinity
integrand = @(x) (1 / (sqrt(2 * pi * sigma2))) .* exp(-((x.^2) / (2 * sigma2)));
P_loznoe(j) = integral(integrand, n2, Inf); % Calculate the integral
end

% Calculate alpha^2 for each sigma^2
alpha2_values ​​= 1 ./sigma2_values; % alpha^2 = 1/sigma^2

% Plot P_false vs. alpha^2
figure;
semilogy(alpha2_values, P_loznoe, ‘r’, ‘LineWidth’, 2); % Logarithmic scale on the Y axis
title(‘False discovery rate vs. alpha^2’);
xlabel(‘alpha^2’);
ylabel(‘P_{false}’);
xlim([10 100]); % Set limits on the X axis
ylim([10^(-8) 10^(-1)]); % Set limits on the Y axis to expand the grid
grid on; % Grid on

But for some reason my graph is not in the specified interval and not in the form of a decreasing exponent, but in the form of a linear decrease.

How can this be fixed?

Thanks in advance! gauss MATLAB Answers — New Questions

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