cdfN2#

Purpose#

Computes the Normal cumulative distribution function over the interval between x and x+dx.

Format#

p = cdfN2(x, dx)#

Parameters:

x (MxN matrix) – Lower limit at which to evaluate the normal cumulative distribution function.
dx (KxL matrix) – ExE conformable to x, intervals used to compute the upper bound, x + dx.

Returns:

p (matrix, max(M,K) by max(N,L)) – The normal cumulative distribution function over the interval \(x\) to \(x + dx\), i.e., \(Pr(x < X < x + dx)\)

Examples#

// Starting x
x = 0;

// Interval
dx = 1.96;

// Call the cdfN2
print cdfN2(x, dx);

After the above code:

0.4750021048517795

// Starting x
x = 1;

// Interval
dx = 0.5;

// Call the cdfN2
print cdfN2(x, dx);

After the above code:

9.1848052662599017e-02

// Starting x
x = 20;

// Interval
dx = 1e-2;

// Call the cdfN2
print cdfN2(x, dx);

After the above code:

5.0038115018684521e-90

// Starting value
x = { 0 0.25   1  -2  -1,
      1    0 0.4 2.3   1,
      3    1 0.9 0.4 0.1 };

dx = { 0.5, 1.4, 2 };

print cdfN2(x, dx);

After the above code:

1915   0.1747   0.0918   0.0441   0.1499
1505   0.4192   0.3086   0.0106   0.1505
0013   0.1573   0.1822   0.3364   0.4423

Remarks#

The relative error is:

\(\left\| x \right\| \leq 1\) and \(dx \leq 1\)	\(\pm 1e-14\)
\(1 < \left\| x \right\| < 37\) and \(\left\| dx \right\| < \frac{1}{\left\| x \right\|}\)	\(\pm 1e-13\)
\(min(x, x + dx) > -37\) and \(y > 1e-300\)	\(\pm 1e-11\) or better

A relative error of \(\pm 1e-14\) implies that the answer is accurate to better than \(±1\) in the 14th digit.