They have a lower likelihood of extreme events compared to a normal distribution. To minimize the risk of large negative events, risk-averse investors can focus on investments whose returns follow a platykurtic distribution.

What does Platykurtosis mean?

platykurtosis (uncountable) (statistics) The property of having kurtosis less than that of a normal distribution; equivalently, having negative excess kurtosis.

What does the kurtosis value tell us?

Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers.

What is Leptokurtic and why is it important in statistics?

When analyzing historical returns, kurtosis can help an investor gauge an asset's level of risk. A leptokurtic distribution means that the investor can experience broader fluctuations (e.g., three or more standard deviations from the mean) resulting in greater potential for extremely low or high returns.

What is the importance of skewness and kurtosis?

“Skewness essentially measures the symmetry of the distribution, while kurtosis determines the heaviness of the distribution tails.” The understanding shape of data is a crucial action. It helps to understand where the most information is lying and analyze the outliers in a given data.

Normal Distributions, Standard Deviations, Modality, Skewness and Kurtosis: Understanding concepts

Why is skewness important?

The primary reason skew is important is that analysis based on normal distributions incorrectly estimates expected returns and risk. ... Knowing that the market has a 70% probability of going up and a 30% probability of going down may appear helpful if you rely on normal distributions.

What can skewness tell us?

Also, skewness tells us about the direction of outliers. You can see that our distribution is positively skewed and most of the outliers are present on the right side of the distribution. Note: The skewness does not tell us about the number of outliers. It only tells us the direction.

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).

How do you determine Leptokurtic?

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

What is an example of a Leptokurtic distribution?

An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian, and therefore produces more outliers than the normal distribution.

How do you interpret kurtosis?

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).

How much kurtosis is acceptable?

The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). Hair et al. (2010) and Bryne (2010) argued that data is considered to be normal if skewness is between ‐2 to +2 and kurtosis is between ‐7 to +7.

How do you interpret skewness and kurtosis in statistics?

A general guideline for skewness is that if the number is greater than +1 or lower than –1, this is an indication of a substantially skewed distribution. For kurtosis, the general guideline is that if the number is greater than +1, the distribution is too peaked.

Is Mesokurtic normal curve?

Mesokurtic distributions have the same kurtosis as that of the normal distribution, or normal curve, also known as a bell curve. In contrast, a leptokurtic distribution has fatter tails. This means that the probability of extreme events is greater than that implied by the normal curve.

Why does Leptokurtic have fatter tails?

This definition is used so that the standard normal distribution has a kurtosis of three. Leptokurtic (Kurtosis > 3): Distribution is longer, tails are fatter. ... The reason for this is because the extreme values are less than that of the normal distribution.

How do I identify Platykurtic?

K < 3 indicates a platykurtic distribution (flatter than a normal distribution with shorter tails). K > 3 indicates a leptokurtic distribution (more peaked than a normal distribution with longer tails). K = 3 indicates a normal “bellshaped” distribution (mesokurtic). K < 3 indicates a platykurtic distribution.

What is Leptokurtic formula?

The formula for kurtosis is expressed as the ratio of the fourth moment and variance (s²) squared or squared the second moment of the distribution. Mathematically, it is represented as, Kurtosis = n * Σⁿ_i(Y_i – Ȳ)⁴ / (Σⁿ_i(Y_i – Ȳ)²)².

What value of kurtosis is Platykurtic?

2.3.

Kurtosis >3 is recognized as leptokurtic and <3. as platykurtic (lepto=thin; platy=broad). There are four different formats of kurtosis, the simplest is the population kurtosis; the ratio between the fourth moment and the variance.

What number is Platykurtic?

The kurtosis of any univariate normal distribution is 3. It is common to compare the kurtosis of a distribution to this value. Distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is "flat-topped" as is sometimes stated.

When talking about a histogram What does skewness refer to?

Skewness is the measure of the asymmetry of a histogram (frequency distribution ). A histogram with normal distribution is symmetrical. In other words, the same amount of data falls on both sides of the mean.

What is the nature of skewness when Mean Median?

The mean, mode and median can be used to figure out if you have a positively or negatively skewed distribution. ... If the mean is greater than the median, the distribution is positively skewed. If the mean is less than the median, the distribution is negatively skewed.

How do you deal with skewed data?

1. log transformation: transform skewed distribution to a normal distribution. ...
2. Remove outliers.
3. Normalize (min-max)
4. Cube root: when values are too large. ...
5. Square root: applied only to positive values.
6. Reciprocal.
7. Square: apply on left skew.

How do you interpret skewness in SPSS?

In SPSS, the skewness and kurtosis statistic values should be less than ± 1.0 to be considered normal. For skewness, if the value is greater than + 1.0, the distribution is right skewed. If the value is less than -1.0, the distribution is left skewed.

Is skewness good or bad?

Skewness provides valuable information about the distribution of returns. However, skewness must be viewed in conjunction with the overall level of returns. Skewness by itself isn't very useful. It is entirely possible to have positive skewness (good) but an average annualized return with a low or negative value (bad).