how to plot a gaussian 1D in matlab

for k = 1 : K 
    ax = linspace(min_x,max_x,100); 
    y = my_gaussian(x,means,vars); 
    plot(ax,y);
end

Answer 1

[Adam Danz]

Parameterized Gaussian distribution function (no toolboxes needed)

This anonymous function produces a normal probability density curve at the values in x with a mean of mu and a standard deviation of sigma.

gausDist = @(x,mu,sig)(1./(sig.*sqrt(2*pi))).*exp((-(x-mu).^2)./(2.*sig.^2));

• x is an array of x-values.
• mu is the mean
• sig is the standard deviation

The anonymous function is equivalent to normpdf(x,mu,sig) (Statistics and Machine Learning Toolbox) except that normpdf returns NaN values when the standard deviation (sig) is negative whereas the anonymous function will evaluate the negative value.

Comparison between normpdf and the anonymous function:

x = -4:.2:6;
mu = -1.5;
sig = 1.8;
y = gausDist(x,mu,sig);
y2 = normpdf(x,mu,sig); 
plot(x,y,'b-','LineWidth',3,'DisplayName','Anonymous fcn')
hold on
plot(x,y2,'r--','LineWidth',3,'DisplayName','normpdf')
legend
grid on
title(sprintf('Guassian with \\mu=%.1f \\sigma=%.1f', mu, sig))

The doc page on the Normal Distribution may also be helpful.

Fully parameterized Gaussian function (no toolboxes needed)

This anonymous function creates a Gaussian curve that includes parameters for amplitude and vertical offset.

gaus = @(x,mu,sig,amp,vo)amp*exp(-(((x-mu).^2)/(2*sig.^2)))+vo;

• x is an array of x-values.
• mu is the mean
• sig is the standard deviation
• amp is the (positive or negative)
• vo is the vertical offset from baseline (positive or negative)

To add noise along the y-axis of the guassian,

y = gaus(___);

yh = y + randn(size(y))*amp*.10; % noise is 10% of the amp

Demo:

x = linspace(-5,25,100);
mu = 10;
sig = 5;
amp = 9;
vo = -5; 
y = gaus(x,mu,sig,amp,vo);
% Plot gaussian
figure()
plot(x, y, 'b-', 'LineWidth',3)
% Add noise
yh = y + randn(size(y))*amp*.10;
hold on
plot(x, yh, 'ro','markersize', 4)
grid on
title(sprintf('Guassian with \\mu=%.1f \\sigma=%.1f amp=%.1f vo=%.1f', ...
    mu, sig, amp, vo))

normpdf from the Statistics and Machine Learning Toolbox

y = normpdf(x,mu,sigma) produces a normal probability density curve at the values in x with a mean of mu and a standard deviation of sigma. Unlike the parameterized anonymous function above, the output to normpdf carries a specifc meaning. Therefore, amplitude and vertical offset are not specified in normpdf.

This demo uses the same argument values as above.

y = normpdf(x,mu,sig); 
figure()
plot(x,y,'-b','LineWidth',3)
grid on

gaussmf from the Fuzzy Logic Toolbox

y = gaussmf(x,[sigma,mu]) produces a Gaussian membership function which differs from the probability density function produced by normpdf. A key difference is that the Gaussian membership function always has a maximum value of 1. Given a sufficiently wide range of x values, the curve ranges from near 0 to 1 along the y axis. Thus, amplitude (amp) and vertical offset (vo) can be applied to the curve by,

y = amp * gaussmf(x,[sigma,mu]) + vo;

This demo uses the same argument values as above and compares gausmf (red) and the parameterized anonymous function (blue).

y = gaus(x,mu,sig,amp,vo);          % parameterized anonymous function
y2 = amp*gaussmf(x,[sig,mu])+vo;    % fuzzy Logic toolbox

figure()
plot(x, y, 'b-', 'LineWidth',3, 'DisplayName','Parameterized fcn')
hold on
plot(x, y2, 'r--', 'LineWidth',4, 'DisplayName','gaussmf()')
grid on
title(sprintf('Guassian with \\mu=%.1f \\sigma=%.1f amp=%.1f vo=%.1f', ...
    mu, sig, amp, vo))
legend()

[Kibum Nam]

very useful. thanks a lot.

Answer 2

[M]

 You can use Matlab function to construct Gaussian function :

 x = 0:0.1:10;
y = gaussmf(x,[2 5]);
plot(x,y)

https://fr.mathworks.com/help/fuzzy/gaussmf.html

[Gadadhar Sahoo]

how to plot using both means and variance for gaussian 1D

[M]

Did you read the documentation ? Those are the second parameter you give to the function gaussmf(x,[sigma,mean]) .

[Gadadhar Sahoo]

i am not getting the gaussian bell curve..here is my code

clc clear load fisheriris [N, M] = size(meas); x = meas(:,1)'; max_x = max(max((x))); min_x = min(min(x)); K = 3; means = min_x + (max_x - min_x)*rand(1, K); vars = ones(1, K); prior = ones(1,K)/K; prob = zeros(N, K); for g = 1 : 1 for p = 1 : N for k = 1 : K gaussian = (1/sqrt(2*pi*vars(k)))*exp(-(x(p)-means(k)).^2/(2*vars(k))); prob(p,k) = gaussian* prior(k); end sum_probs = sum(prob(p,:)); prob(p,:) = prob(p,:)/sum_probs; end for k = 1 : K means(k) = sum(prob(:,k)'.*x)/N; vars(k) = sum(prob(:,k)'.*(x - means(k)).^2)/N; prior(k) = sum(prob(:,k))/N; end end figure scatter(x,zeros(1,N)); hold on for k = 1 : K ax = linspace(min_x,max_x,100); y = gaussmf(ax,[means,vars]); plot(ax,y);

end

[Chad MacDonald]

Do not use the gaussmf function from Fuzzy Logic Toolbox to compute a Gaussian distribution. This function evaluates a Gaussian membership function for a fuzzy logic system, which is not the same thing as a Gaussian distribution. For more information on Gaussian probability distributions, see Normal Distribution.

Answer 3

[Chad MacDonald]

If you have Statistics and Machine Learning Toolbox, you can compute a Gaussian probability distributon using the normpdf function. For example, the following code computes and plots a normal distribution with a mean of 5 and a standard deviation of 1.

x = 0:0.1:10;
mu = 5;
sigma = 1;
y = normpdf(x,mu,sigma);
plot(x,y)