# XCONF

## Purpose:

Returns X value for a given density function and confidence level.

## Syntax:

XCONF(pdens, c, interp)

pdens

-

A series. The probability density function or histogram series.

c

-

A real or series. The confidence level or percentile (0.0 <= c <= 1.0).

interp

-

Optional. An integer, the X value linear interpolation flag:

 0: Do not interpolate X value 1: Linearly interpolate X value if necessary (default)

## Returns:

A real or series, the X (or z) value for the distribution given the input probability level.

## Example:

W1: gnorm(10000, 1, 5)

W2: histogram(W1, 1000)

xconf(W2, 0.5)

returns 4.989789, the approximate mean of the original series.

## Example:

W1: pdfnorm(-8..0.001..8)

W2: pdfnorm({-2, -1, 0, 1, 2})

W3: xconf(w1, w2)

W4: invprobn(w2)

W1 contains 16001 samples of normal distribution with a mean of 0 and a standard deviation of 1.

W2 contains the series {0.022750, 0.158655, 0.500000, 0.841345, 0.977250}, the confidence level at X values {-2, -1, 0, 1, 2} for a normal distribution.

W3 contains the series {-2, -1, 0, 1, 2}, the X values for the confidence levels in W2.

W4 contains the series {-2, -1, 0, 1, 2}, the X values for the confidence levels in W2.

Both W3 and W4 contain X values for the confidence levels {0.022750, 0.158655, 0.500000, 0.841345, 0.977250} for the normal distribution. W3 looks up the values from the cumulative distribution derived from W1 and W4 uses INVPROBN to compute the X values assuming a normal distribution.

## Remarks:

The cumulative distribution derived from the input density function or histogram is automatically normalized between 0 and 1.

XCONF returns NA if the confidence level is out of range.

Unless specified, XCONF automatically performs linear interpolation to find the best X value for a given confidence level if an exact match is not found.

See CONFX to return a confidence level for a density function and X value.

See INVPROBN to compute the X value for a normal distribution.