KURTOSIS

The numerical values to compute the kurtosis of. This can be a constant value, a column, a cell range, or an expression evaluating to any of the above. For the format definition of data, see the "Macro Function Parameters" section in the chapter in this guide for your IBM® product. There must be at least four values in data.

keyword

This optional keyword determines how the computation is performed over the input data range. Select one of the following:

ALL

Performs the computation on all cells in data (default)

COL

Performs the computation separately for each column of data

ROW

Performs the computation separately for each row of data

For more details on using keywords in IBM® Campaign, see Format Specifications.

For more details on using keywords in IBM® PredictiveInsight, see Format Specifications.

Description

KURTOSIS calculates the kurtosis of the values in the specified data range. Kurtosis is a measurement of the relative peakedness or flatness of a distribution compared to a normal distribution. The more negative the kurtosis is, the flatter the distribution. The more positive the kurtosis is, the sharper the peak of the distribution.

The kurtosis is calculated as follows:

where n is the number of samples in the distribution, mean is the average, and ? is the standard deviation of the distribution. A minimum of three data values must be provided to compute kurtosis.

Examples

TEMP = KURTOSIS(MERGE(3, 4, 5)) or TEMP = KURTOSIS(MERGE(3, 4, 5), ALL)

Creates a new column named TEMP containing the value -1.5.

TEMP = KURTOSIS(V1)

Creates a new column named TEMP containing a single value which is the kurtosis of the contents of column V1.

TEMP = KURTOSIS(V1:V3)

Creates a new column named TEMP containing a single value which is the kurtosis of the contents of columns V1, V2, and V3.

TEMP = KURTOSIS(V1[10:20])

Creates a new column named TEMP containing a single value which is the kurtosis of the cells in rows 10-20 of column V1.

TEMP = KURTOSIS(V1[1:5]:V4)

Creates a new column named TEMP containing a single value which is the kurtosis of the cells in rows 1-5 of columns V1 through V4.

TEMP = KURTOSIS(V1:V3, COL)

Creates three new columns named TEMP, VX, and VY. The single value in the TEMP column is the kurtosis of the contents of column V1, the single value in the VX column is the kurtosis of the contents of column V2, and the single value in the VY column is the kurtosis of the contents of column V3.

TEMP = KURTOSIS(MERGE(1,4), COL)

Creates two new columns named TEMP and VX, each containing the value -3.

TEMP = KURTOSIS(V1[1:5]:V3, COL) or TEMP = KURTOSIS(V1[1:5]:V3[1:5], COL)

Creates three new columns named TEMP, VX, and VY, each containing a single value. The value in column TEMP is the kurtosis of the cells in rows 1-5 of column V1, the value in column VX is the kurtosis of the cells in rows 1-5 of column V2, and the value in column VY is the kurtosis of the cells in rows 1-5 of column V3.

TEMP = KURTOSIS(V1:V3, ROW)

Creates a new column named TEMP where each cell entry is the kurtosis of the corresponding row across columns V1, V2, and V3.

TEMP = KURTOSIS(V1[1:5]:V3],ROW) or TEMP = KURTOSIS(V1[1:5]:V3[1:5], ROW)

Creates a new column named TEMP, where the cells in rows 1-5 contain the kurtosis of the corresponding row across columns V1 through V3. The other cells in TEMP are empty.

Related Functions

Function	Description
STAT	Computes the first through fourth moments of the specified data range
SKEW	Computes the skew of the distribution of a range of cells
STDV or STDEV	Computes the standard deviation of a range of cells
VARIANCE	Computes the variance of a range of cells