# lncdfn2#

## Purpose#

Computes natural log of interval of Normal cumulative distribution function.

## Format#

y = lncdfn2(x, dx)#
Parameters:
• x (MxN matrix) – values at which to evaluate the cumulative distribution function.

• dx (KxL matrix) – ExE conformable with x, intervals used to compute the upper bound, x + dx.

Returns:

lnp (max(M,K) x max(N,L) matrix) –

the log of the integral from x to x+dx of the Normal distribution, i.e.,

$ln\ Pr(x < X < x+dx)$

## Examples#

// Set x
x = -10;

// Set interval
dx = 29;

print
lncdfN2(x, dx);

-7.6198530241605269e-24

// Set x
x = 0;

// Set interval
dx = 1;

print
lncdfN2(x, dx);

-1.0748623268620716e+00

// Set x
x = 5;

// Set interval
dx = 1;

print
lncdfN2(x, dx);

-1.5068446096529453e+01


## Remarks#

The relative error is:

 $$\|x\| < 1$$ and $$dx < 1$$ ±1e-14 $$1 < \|x\| < 37$$ and $$\|dx\| < 1/\|x\|$$ ±1e-13 $$min(x,x+dx) > -37$$ and $$y > -690$$ ±1e-11 or better

A relative error of ±1e-14 implies that the answer is accurate to better than ±1 in the 14th digit after the decimal point.

## Source#

lncdfn.src

Functions cdfn2()`