Definition of Kurtosis
Like
skewness, kurtosis is a statistical measure that is used to describe the
distribution. Whereas skewness
differentiates extreme values in one versus to other tail, kurtosis measures
extreme values in either tail. Distributions
with large kurtosis exhibit tail data exceeding the tails of normal
distribution. Distribution with low
kurtosis exhibit tail data that is generally less extreme than the tails of the
normal distribution. Kurtosis is a
measure of the combined weight of a distributions tails relative to the center
of the distribution. When a set of
approximately normal data is graphed via a histogram, it shows a bell peak and
most data within + or –three standard deviations of the mean. However, when high kurtosis is present, the
tails extend farther than the + or – three standard deviations of the normal
bell-curved distributions. Kurtosis is
confused with a measure of the peakedness of a distribution. However, kurtosis is a measure that describes
the shape of a distribution’s tails in relation to its overall shape. A distribution can be infinitely peaked with
low kurtosis, and a distribution can be perfectly flat-topped with infinite
kurtosis. Thus, kurtosis measures
“tailedness”, not “peakedness”.
Types of Kurtosis
There
are three categories of kurtosis that can be displayed by a set of data. All measures of kurtosis are compared against
a standard normal distribution, or bell curve. The first category of kurtosis is a mesokurtic
distribution. This distribution has
kurtosis statistic similar to that of the normal distribution, meaning that the
extreme value characteristic of the distribution similar to that of a normal
distribution. The second category is
leptokurtic distribution. Any
distribution that is leptokurtic displays greater kurtosis than a mesokurtic
distribution. The final type of distribution is a platykurtic distribution.
These types of distributions have short tails.
Figure 1. Types of Kurtosis
Table 1
Types of kurtosis and values
Sl No
|
Types of Kurtosis
|
Value
|
1
|
Mesokurtic
|
0.263
|
2
|
Leptokurtic
|
<0.263
|
3
|
Platykurtic
|
>0.263
|
Applications of kurtosis.
Kurtosis
is a useful measure of whether there is a problem with outliers in a data
set. Larger kurtosis indicates a more
serious outlier problem and may lead the researcher to choose alternative
statistical methods.
POWER POINT ON KURTOSIS
