# 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:

0.1915   0.1747   0.0918   0.0441   0.1499
0.1505   0.4192   0.3086   0.0106   0.1505
0.0013   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.

Functions lncdfn2()