Skewness and Kurtosis

1. Skewness and Kurtosis

2. Skewness
• Skewness essentially is a commonly used measure in
descriptive statistics that characterizes the asymmetry
of a data distribution.
• It provides information about the shape of the
distribution and the extent to which it deviates from
symmetry.
• In a symmetrical distribution, the values are evenly
distributed around the mean, resulting in a skewness
value of zero.
• in an asymmetric distribution, the values tend to be
concentrated on one side of the mean, causing the
distribution to be skewed.

3. • Skewness can help identify whether the tail of the
distribution is elongated to the left (negative skewness) or
to the right (positive skewness).
• Positive skewness (right-skewed distribution): In a
positively skewed distribution, the tail on the right side of
the distribution is longer or stretched out compared to the
left side. This means that the majority of the data points
are concentrated towards the lower values, and there are a
few extreme high values.
• Negative skewness (left-skewed distribution): In a
negatively skewed distribution, the tail on the left side of
the distribution is longer or stretched out compared to the
right side. This means that the majority of the data points
are concentrated towards the higher values, and there are
a few extreme low values.

4. Positive Skewness
Negative Skewness

6. Skewness Coefficient
• Skewness can be calculated using various methods,
whereas the most commonly used method is Pearson’s
coefficient.
• Pearson’s coefficient of skewness:

7. Kurtosis
• Kurtosis is a statistical measure that describes the shape
and peakedness of a probability distribution. It provides
information about the tails of the distribution and the
presence of outliers.
• Kurtosis measures the degree to which the distribution of
a variable deviates from a normal distribution (also
known as the Gaussian distribution or bell curve). A
normal distribution has a kurtosis value of 0.

8. • Positive kurtosis (leptokurtic distribution): A positively
kurtotic distribution has heavier tails and a higher peak
compared to a normal distribution. It indicates that the data
has more extreme values or outliers than would be expected
in a normal distribution. This means that there is a higher
probability of extreme values occurring.
• Negative kurtosis (platykurtic distribution): A negatively
kurtotic distribution has lighter tails and a flatter peak
compared to a normal distribution. It indicates that the data
has fewer extreme values or outliers than would be expected
in a normal distribution. This means that extreme values are
less likely to occur.
• Excess kurtosis: Kurtosis is often reported as excess kurtosis,
which is the kurtosis value minus 3. This adjustment allows
the normal distribution to have an excess kurtosis value of 0.

9. • Types of Excess Kurtosis
– Leptokurtic or heavy-tailed distribution (kurtosis more
than normal distribution)
– Mesokurtic (kurtosis same as the normal distribution)
– Platykurtic or short-tailed distribution (kurtosis less
than normal distribution)
Leptokurtic (Kurtosis > 3)
Platykurtic (Kurtosis < 3)
Mesokurtic (Kurtosis = 3)