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()