Maple Professional
Maple Academic
Maple Student Edition
Maple Personal Edition
Maple Player
Maple Player for iPad
MapleSim Professional
MapleSim Academic
Maple T.A. - Testing & Assessment
Maple T.A. MAA Placement Test Suite
Möbius - Online Courseware
Machine Design / Industrial Automation
Aerospace
Vehicle Engineering
Robotics
Power Industries
System Simulation and Analysis
Model development for HIL
Plant Modeling for Control Design
Robotics/Motion Control/Mechatronics
Other Application Areas
Mathematics Education
Engineering Education
High Schools & Two-Year Colleges
Testing & Assessment
Students
Financial Modeling
Operations Research
High Performance Computing
Physics
Live Webinars
Recorded Webinars
Upcoming Events
MaplePrimes
Maplesoft Blog
Maplesoft Membership
Maple Ambassador Program
MapleCloud
Technical Whitepapers
E-Mail Newsletters
Maple Books
Math Matters
Application Center
MapleSim Model Gallery
User Case Studies
Exploring Engineering Fundamentals
Teaching Concepts with Maple
Maplesoft Welcome Center
Teacher Resource Center
Student Help Center
stats[describe,kurtosis] - Moment Coefficient of Kurtosis
Calling Sequence
stats[describe, kurtosis](data)
stats[describe, kurtosis[Nconstraints]](data)
describe[kurtosis](data)
describe[kurtosis[Nconstraints]](data)
Parameters
data
-
statistical list
Nconstraint
(optional, default=0) Number of constraints, 1 for sample, 0 for full population
Description
Important: The stats package has been deprecated. Use the superseding package Statistics instead.
The function kurtosis of the subpackage stats[describe, ...] computes the moment coefficient of kurtosis of the given data. It is defined to be the fourth moment about the mean, divided by the fourth power of the standard deviation.
The kurtosis measures the degree to which a distribution is flat or peaked. For the normal distribution (mesokurtic), the kurtosis is 3. If the distribution has a flatter top (platykurtic), the kurtosis is less than 3. If the distribution has a high peak (leptokurtic), the kurtosis is greater than 3.
Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.
The definition of standard deviation varies according to whether it is computed for the whole population, or only for a sample. It follows then that the kurtosis also depends on this factor, which is controlled by the parameter Nconstraint. For more information on this, refer to describe[standarddeviation].
There are other possibilities for the definition of the kurtosis, as can be seen in various books on statistics.
The command with(stats[describe],kurtosis) allows the use of the abbreviated form of this command.
Examples
This data has a flatter distribution than the normal distribution.
This data has about the same flatness as the normal distribution.
This data is more sharply peaked that then normal distribution.
Note that these three examples have a symmetrical distribution. Their skewness is then equal to zero. They are not distinguishable from the normal distribution according to the skewness, but they are according to the kurtosis.
See Also
describe(deprecated)[moment], describe(deprecated)[skewness], describe(deprecated)[standarddeviation], describe(deprecated)[variance], Statistics, Statistics[Kurtosis], stats(deprecated)[data], transform(deprecated)[classmark]
Download Help Document
