erfinv

erfinv(0.25)

ans = 
0.2253

For inputs outside [-1,1], erfinv returns NaN. For -1 and 1, erfinv returns -Inf and Inf, respectively.

erfinv([-2 -1 1 2])

ans = 1×4

   NaN  -Inf   Inf   NaN

Find the inverse error function of the elements of a matrix.

M = [0 -0.5; 0.9 -0.2];
erfinv(M)

ans = 2×2

         0   -0.4769
    1.1631   -0.1791

Plot the inverse error function for -1 < x < 1.

x = -1:0.01:1;
y = erfinv(x);
plot(x,y)
grid on
xlabel('x')
ylabel('erfinv(x)')
title('Inverse Error Function for -1 < x < 1')

Generate Gaussian distributed random numbers using uniformly distributed random numbers. To convert a uniformly distributed random number $$x$$ to a Gaussian distributed random number $$y$$, use the transform

Note that because x has the form -1 + 2*rand(1,10000), you can improve accuracy by using erfcinv instead of erfinv. For details, see Tips.

Generate 10,000 uniformly distributed random numbers on the interval [-1,1]. Transform them into Gaussian distributed random numbers. Show that the numbers follow the form of the Gaussian distribution using a histogram plot.

rng('default')
x = -1 + 2*rand(1,10000);
y = sqrt(2)*erfinv(x);
h = histogram(y);