Area(R,I,X1,X2)

Returns the area (sum of trapezoids) under array R across index I between X1 and X2. X1 and X2 are optional.

Declaration

Area( R : Numeric[J] ; I : ascending Numeric[J] ; X1,X2 : opt numeric atomic ; J : opt hidden IndexType = I )

Simplest Usage

In the simple usage, the second parameter, I, is an index with increasing numeric values, and R is indexed by I. You can visualize R as a function of I, and Area returns the area under the curve obtained when I is plotted on the X-axis and R on the Y-axis.

Using an array for I

(new to 4.0). When your X-axis values are in an array, e.g., X and Y are both arrays indexed by In1, you can use:

Area( Y,X,X1,X2,In1 )

Here the x-axis values are taken from the X-array rather than from the index. If X1 and X2 are omitted, you can write

Area( R:Y,I:X,J:In1 )

or equivalently

Area( Y,X, J:In1 )

When using an array of values for the X-axis, the index, J, may contain arbitrary values, but X must contain values that are in ascending order.

If X is a self-indexed array, and Y is indexed by X, and the J parameter is omitted, then the values of X are used and the self-index of X is used.

Details

Some notes: J is hidden from the user, since the main concern was fixing several bugs with the function while maintaining backward compatibility. However, as the above example shows, it can be useful. The second parameter is named I for legacy reasons, but it would be better named X with the J parameter named I. Consider this change when updating manuals.

Another difference relative to 3.1 is that X2 (upper bound) can be specified while not specifying X1 (lower bound). So, for example, you could find the area up to a given point, e.g.:

var dens := Pdf(Ch1);
Area( dens, dens.Step, X2:x )