Is Leptokurtic a normal distribution?

Is Leptokurtic a normal distribution?

Leptokurtic distributions are distributions with positive kurtosis larger than that of a normal distribution. A normal distribution has a kurtosis of exactly three. Therefore, a distribution with kurtosis greater than three would be labeled a leptokurtic distribution.

What does it mean if a data set has a Leptokurtic distribution?

A leptokurtic distribution has excess positive kurtosis, where the kurtosis is greater than 3. The tails are fatter than the normal distribution.

Is Platykurtic distribution normal?

The term “platykurtic” refers to a statistical distribution in which the excess kurtosis value is negative. For this reason, a platykurtic distribution will have thinner tails than a normal distribution will, resulting in fewer extreme positive or negative events.

How do you interpret a negative kurtosis?

Negative values of kurtosis indicate that a distribution is flat and has thin tails. Platykurtic distributions have negative kurtosis values. A platykurtic distribution is flatter (less peaked) when compared with the normal distribution, with fewer values in its shorter (i.e. lighter and thinner) tails.

How to make this leptokurtic data normal again?

Hence your data can be well described by a Lambert W × Gaussian distribution with input X ∼ N ( 2000, 400) and a tail parameter of δ = 0.2 (which implies that only moments up to order ≤ 5 exist). Now back to your question: how to make this leptokurtic data normal again?

Is there a transformation ( s ) for normalizing kurtotic data?

I think this is also called the normal score transformation. It is a great method in that it can transform any distribution into the normal. Unfortunately, I do not believe it is monotonic and hence, there is no back transformation.

Is the kurtosis of YY a leptokurtic distribution?

The qqplot of yy is very close to your qqplot in the original post and the data is indeed slightly leptokurtic with a kurtosis of 5. Hence your data can be well described by a Lambert W × Gaussian distribution with input X ∼ N ( 2000, 400) and a tail parameter of δ = 0.2 (which implies that only moments up to order ≤ 5 exist).

Which is more reliable value at risk or leptokurtic distribution?

In general, the fewer the kurtosis and the greater the confidence within each, the more reliable and safer a value at risk distribution is. Leptokurtic distributions are known for going beyond three kurtoses. This typically decreases the confidence levels within the excess kurtosis, creating less reliability.