Contents
How do you know if a distribution is Leptokurtic?
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 is Leptokurtic and Platykurtic?
Leptokurtic: More values in the distribution tails and more values close to the mean (i.e. sharply peaked with heavy tails) Platykurtic: Fewer values in the tails and fewer values close to the mean (i.e. the curve has a flat peak and has more dispersed scores with lighter tails).
What does positively skewed mean?
Understanding Skewness These taperings are known as “tails.” Negative skew refers to a longer or fatter tail on the left side of the distribution, while positive skew refers to a longer or fatter tail on the right. The mean of positively skewed data will be greater than the median.
How do you know if kurtosis is significant?
If the kurtosis is greater than 3, then the dataset has heavier tails than a normal distribution (more in the tails). If the kurtosis is less than 3, then the dataset has lighter tails than a normal distribution (less in the tails).
Is it possible to have a unconditional leptokurtosis?
For measuring value-at-risk, we are interested in modeling the conditional distributions of key factors, but histograms such as Exhibit 7.8 are more descriptive of unconditional distributions. 3 Is it possible for a stochastic process to have leptokurtic unconditional distributions but non-leptokurtic conditional distributions? Certainly.
What is the meaning of leptokurtic kurtosis analysis?
Leptokurtic is one of three major categories found in kurtosis analysis. Its other two counterparts are mesokurtic and platykurtic. Leptokurtic distributions are distributions with positive excess kurtosis beyond that of a normal distribution.
How are log returns modeled with leptokurtosis?
For commodities or energy products, such leptokurtosis is often extreme. It has prompted some authors to propose that log returns be modeled with leptokurtic distributions. For example, Wilson ( 1993) proposes that key factors for value-at-risk measures be modeled with Student t distributions.
Is the histogram of returns highly leptokurtic?
The histogram of returns is highly leptokurtic. This leptokurtosis is not an isolated result. Histograms of log returns for financial assets often exhibit leptokurtosis. For commodities or energy products, such leptokurtosis is often extreme. It has prompted some authors to propose that log returns be modeled with leptokurtic distributions.