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

See also

Functions cdfn2()