# Measures of sample skewness and kurtosis

Platykurtic-distributed assets and markets may appeal to risk-averse investors since they are less likely to produce extreme outcomes. The word “platykurtic” refers to a statistical distribution where the value of excess kurtosis is negative. A platykurtic distribution would, therefore, have thinner tails than a normal distribution, leading to less extreme positive or negative events. While mesokurtic distributions have kurtosis of three, leptokurtic and platykurtic distributions have optimistic and negative extra kurtosis, respectively. For a sample size of 100 or larger, an excess kurtosis of greater than one is considered unusually high. Based on the above table, let us now calculate the possible veblen goods are basically range of log returns within which Nifty could trade over the next one month. A negative value means that you have light-tails (i.e. little data in your tails).

## Fundamental Analysis

Characteristics of this type of distribution is one with lengthy tails (outliers.) The prefix of “lepto-” means “skinny,” making the shape of a leptokurtic distribution easier to remember. Examples of leptokurtic distributions are the T-distributions https://1investing.in/ with small degrees of freedom. Kurtosis is all about the tails of the distribution — not the peakedness or flatness. A massive pattern can yield a statistically important non-normality even if the departure from normality is, substantively, trivial.

You might have heard of the term ‘bell curve’, a curve that resembles the shape of a bell when plotted on a chart. In statistics, bell curve is frequently used to illustrate normal distribution, which is a type of statistical distribution that is symmetrical about its mean. The chart below depicts how a normal distribution looks like – resembling a bell-shaped curve that is spaced evenly on either side of the mean (µ), which is represented by the vertical line. If the kurtosis is less than zero, then the distribution is mild tails and is called a platykurtic distribution. If the kurtosis is larger than zero, then the distribution has heavier tails and is known as a leptokurtic distribution.

## Kurtosis – Types of Kurtosis | Business Statistics

If the 2 are equal, it has zero skewness or a symmetrical distribution. An understanding of the skewness of the dataset signifies whether potential deviations from the imply are going to be constructive or negative. Skewness is computed as the average cubed deviation from the mean standardized by dividing the standard deviation cubed to make the measure free of scale. The skewness is positive for positively skewed distribution, negative for negatively skewed distribution, and zero for symmetrical distribution. Skewness may be quantified as a illustration of the extent to which a given distribution varies from a traditional distribution.

• Meanwhile, for return distributions that are platykurtic (short-tailed distribution), the outliers would be smaller than those found even in normal distribution.
• Investment returns are more likely to have a Platykurtic distribution in the financial context, since there is a small chance that the investment will experience extreme returns.
• And bear in mind, the more data you’ve, the higher you possibly can describe the form of the distribution.
• The UGC NET CBT exam will consist of two papers – Paper I and Paper II. Paper I will be conducted of 50 questions and Paper II will be held for 100 questions.

This number is related to the tails of the distribution, not its peak; hence, the typically-seen characterization of kurtosis as “peakedness” is inaccurate. The test I often use is the Jarque-Bera test of normality of distribution which is predicated not simply on skewness and kurtosis. It is predicated on a composite function of skewness, kurtosis, diploma of freedom and variety of regressors. That sounds more practical than just contemplating a confidence interval of skewness or kurtosis. Looking at simply the skewness or the kurtosis and evaluating them with zero or 3 that are the conventional distribution respective values sounds naive.

## More Business Statistics and Research Methods Questions

T-distributions with tiny degrees of freedom are examples of leptokurtic distributions. Kurtosis is a statistical measure of distribution that is used to characterize it. Unlike skewness, which distinguishes extreme values in one tail from those in the other, kurtosis assesses extreme values in both tails. Tail data exceeds the tails of the normal distribution in distributions with strong kurtosis. In the above table, notice that Tata Motors had the highest standard deviation as well as the highest excess kurtosis. This means that since the start 2021 till the time of writing, compared to the other two stocks, Tata Motors not only had higher dispersion around the mean return but also had longer tails.

• In finance, a leptokurtic distribution exhibits that the investment returns may be susceptible to extreme values on both facet.
• And the .0001Cauchy + .9999U distribution appears perfectly flat over 99.99% of the observable data, but has infinite kurtosis.
• A distribution that is less peaked than a normal distribution is called platykurtic.
• Leptokurtic distributions are prone to extreme values on either side of an investment return.
• Based on the above, what do you think will be the range of returns for Nifty over the next one month, which is roughly equivalent to 21 trading sessions?

Kurtosis is a measure of the mixed weight of a distribution’s tails relative to the center of the distribution. Skewness essentially measures the symmetry of the distribution, while kurtosis determines the heaviness of the distribution tails. So, do not put much emphasis on skewness and kurtosis values you may see. Uniform distributions are platykurtic and have broad peaks, however the beta (.5,1) distribution is also platykurtic and has an infinitely pointy peak. The reason each these distributions are platykurtic is that their extreme values are lower than that of the traditional distribution.

## Types of Kurtosis

Some researchers believe that investors should prefer positive skewness and should avoid negative skewness. For a sample size of 100 or larger, a skewness coefficient of ±0.5 is considered unusually large. Therefore, a distribution with kurtosis greater than three would be labeled a leptokurtic distribution.

In general, leptokurtic distributions have heavier tails or a higher probability of extreme outlier values when compared to mesokurtic or platykurtic distributions. Many financial fashions that try to predict the long run performance of an asset assume a normal distribution, in which measures of central tendency are equal. If the data are skewed, this kind of model will all the time underestimate skewness risk in its predictions. The extra skewed the information, the less correct this financial model might be.

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