Skewness & Kurtosis

29 Nov, 2020

What is skewness?

• Skewness is a asymmetry in a statistical distribution.
• In skewed data, curve is distorted or skewed in left hand side or right hand side.

normal distribution

• In normal distribution, Curve is symmetric, a bell shaped curve.The central tendency of the distribution is same.
• In a perfect normal distribution (standard normal distribution) the curve on the left hand side is the mirror image of the curve on the right hand side.
• we will briefly discuss normal description later...

positive skeweness

• when a distribution skewed to the right.
• The tail on the curve's on the right hand side is longer than the tail on the curve's left hand side.
• Mean is greater than the mode.

Negative skewness

• When distribution skewed to the left.
• The tail on the curve's left hand side is longer than the tail of the curve's right hand side.
• Mean is less than the mode.

If our data is skewed whether it is Negative or positive skewed, that means our data is affected by outliers. We always try to transform our data into normal distribution (symmetric) so that the data is evenly distributed.

What is Kurtosis ?

• Along with skewness, kurtosis is an important descriptive statistic of data distribution.
• Kurtosis tells how heavily tails of a distribution is differ from normal distribution.

In finance, kurtosis is used as a measure of financial risk. A large kurtosis is associated with a high level of risk for an investment because it indicates that there are high probabilities of extremely large and extremely small returns. On the other hand, a small kurtosis signals a moderate level of risk because the probabilities of extreme returns are relatively low.

Mesokurtic

If data follows a normal distribution that means it follows as Mesokurtic distribution.

LeptoKurtic

LeptoKurtic distribution shows heavy tails on either right hand side or left hand side, indicating outliers.

Platykurtic

Platykurtic distribution shows flat tails on either LHS or RHS.

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Skewness essentially measures the symmetry of the distribution,
while kurtosis determines the heaviness of the distribution tails.

Measure of dispersion >