KURTOSIS
Purpose
Returns the kurtosis of the distribution of value_expression.
Syntax
where:
|
Syntax element … |
Specifies … |
|
ALL |
to include all non-null values specified by value_expression, including duplicates, in the computation. This is the default. |
|
DISTINCT |
to exclude duplicates specified by value_expression from the computation. |
|
value_expression |
a literal or column expression for which the kurtosis of the distribution of its values is to be computed. The expression cannot contain any ordered analytical or aggregate functions. |
ANSI Compliance
This is a Teradata extension to the ANSI SQL:2011 standard.
Definition
Kurtosis is the fourth moment of a distribution. It is a measure of the relative peakedness or flatness compared with the normal, Gaussian distribution.
The normal distribution has a kurtosis of 0.
Positive kurtosis indicates a relative peakedness of the distribution, while negative kurtosis indicates a relative flatness.
Result Type and Attributes
The data type, format, and title for KURTOSIS(x) are as follows.
|
Data Type |
Format |
Title |
|
REAL |
Default format of the REAL data type |
Kurtosis(x) |
For information on the default format of data types, see “Data Type Formats and Format Phrases” in SQL Data Types and Literals.
Support for UDTs
By default, Teradata Database performs implicit type conversion on a UDT argument that has an implicit cast that casts between the UDT and any of the following predefined types:
To define an implicit cast for a UDT, use the CREATE CAST statement and specify the AS ASSIGNMENT clause. For more information on CREATE CAST, see SQL Data Definition Language.
Implicit type conversion of UDTs for system operators and functions, including KURTOSIS, is a Teradata extension to the ANSI SQL standard. To disable this extension, set the DisableUDTImplCastForSysFuncOp field of the DBS Control Record to TRUE. For details, see Utilities: Volume 1 (A-K).
For more information on implicit type conversion of UDTs, see Chapter 13: “Data Type Conversions.”
Computation
The equation for computing KURTOSIS is defined as follows:
where:
|
This variable … |
Represents … |
|
x |
value_expression |
Conditions That Produce a NULL Return Value
The following conditions produce a null return value: