通过使用randn
函数,我想创建一个高斯随机变量X
,使得X ~ N(2,4)
并将该模拟PDF与理论曲线一起绘制。
Matlab randn
generates realisations from a normal distribution with zero mean and a standard deviation of 1. Samples from any other normal distribution can simply be generated via:
numSamples = 1000;
mu = 2;
sigma = 4;
samples = mu + sigma.*randn(numSamples, 1);
You can verify this by plotting the histogram:
figure;hist(samples(:));
See the matlab help .
N = 1000;
x = [-20:20];
samples = 2 + 4*randn(N, 1);
ySamples = histc(samples,x) / N;
yTheoretical = pdf('norm', x, 2, 4);
plot(x, yTheoretical, x, ySamples)
randn(N, 1)
creates an N
-by-1 vector.
histc
is histogram count by bins given in x
- you can use hist
to plot the result immediately, but here we want to divide it by N
.
pdf
contains many useful PDFs, normal is just one example.
remember this: X ~ N(mean, variance)
randn in matlab produces normal distributed random variables W with zero mean and unit variance. To change the mean and variance to be the random variable X (with custom mean and variance), follow this equation: X = mean + standard_deviation*W Please be aware of that standard_deviation is square root of variance.
N = 1000;
x = [-20:20];
samples = 2 + sqrt(4)*randn(N, 1);
ySamples = histc(samples,x) / N;
yTheoretical = pdf('norm', x, 2, sqrt(4)); %put std_deviation not variance
plot(x, yTheoretical, x, ySamples)
A quick and easy way to achieve this using one line of code is to use :
mu = 2;
sigma = 2;
samples = normrnd(mu,sigma,M,N);
This will generate an MxN matrix, sampled from N(μ,𝜎)
, ( = N(2,2)
in this particular case). For additional information, see normrnd
.
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