The standard normal distribution has a kurtosis of 3, so if your values are close to that then your graph’s tails are nearly normal. Now that we have a way to calculate kurtosis, we can compare the values obtained rather than shapes. The normal distribution is found to have a kurtosis of three.

Rather, it means the distribution produces fewer and/or less extreme outliers than the normal distribution. An example of a platykurtic distribution is the uniform distribution, which does not produce outliers. Distributions with a positive excess kurtosis are said to be leptokurtic.

A distribution with kurtosis greater than three is leptokurtic and a distribution with kurtosis less than three is platykurtic. A platykurtic https://1investing.in/ distribution has a lower peak and wider bell shape. It will also have longer and shorter tails than a normal distribution.

Signs You Work With a distribution is said to be platy-kurtic when

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On the low end of the spectrum were cash and international bonds, which had excess kurtosis of -1.43 and 0.58, respectively. On the other end of the spectrum were U.S. high-yield bonds and hedge-fund arbitrage strategies, offering excess kurtosis of 9.33 and 22.59. Yarilet Perez is an experienced multimedia journalist and fact-checker with a Master of Science in Journalism. She has worked in multiple cities covering breaking news, politics, education, and more. Her expertise is in personal finance and investing, and real estate. Chip Stapleton is a Series 7 and Series 66 license holder, CFA Level 1 exam holder, and currently holds a Life, Accident, and Health License in Indiana.

Where the probability mass is concentrated in the tails of the distribution. Alternatively it can be seen to be a measure a distribution is said to be platy kurtic when of the dispersion of Z around +1 and −1. Κ attains its minimal value in a symmetric two-point distribution.

One obtains the standard normal density as the limiting distribution, shown as the black curve. Where X is a random variable, μ is the mean and σ is the standard deviation. There is no upper limit to the kurtosis of a general probability distribution, and it may be infinite. Negative excess equals lighter tails than a normal distribution.

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It is a frequency distribution for which beta two equal to 3. The frequency curve has a longer tail on the right of the mode, it is prove that is a positively skewed distribution. IfY2 0, it will give a more flat-topped or a platy kurtic curve. D’Agostino’s K-squared test is a goodness-of-fit normality test based on a combination of the sample skewness and sample kurtosis, as is the Jarque–Bera test for normality.

• The cokurtosis between pairs of variables is an order four tensor.
• Along with skewness, kurtosis is an important descriptive statistic of data distribution.
• The list included a wide range of investments, from U.S. and international equities to real estate, commodities, cash, and bonds.
• The sample kurtosis is a useful measure of whether there is a problem with outliers in a data set.
• Kurtosis isn’t just a theory confined to mathematical textbooks; it has real life applications, especially in the world of economics.

Platykurtic distributions are those with negative excess kurtosis. In addition to this, the discrete probability distribution from a single flip of a coin is platykurtic. The company Black Belt was reviewing the graphical output of her data to see if it was normally distributed so she could easily do the needed statistical calculations. Along with skewness, kurtosis is an important descriptive statistic of data distribution. However, the two concepts must not be confused with each other.

How to Classify the Kurtosis of Distributions

It means the generated returns can either be very high or very low as per the outliers in the distribution. When negative, it indicates that the deviation of the mean data set from the mean is flat. The following figures show charts of these three types of distributions, all with the same standard deviation. This technique is known as a quantile-quantile plot, or Q-Q for short. To answer these kinds of questions we need not just a qualitative description of kurtosis, but a quantitative measure. The formula used is μ4/σ4 where μ4 is Pearson’s fourth moment about the mean and sigma is the standard deviation.

The following illustration1 shows a leptokurtic distribution along with a normal distribution . Leptokurtic distributions are known for going beyond three kurtoses. This typically decreases the confidence levels within the excess kurtosis, creating less reliability.

A leptokurtic distribution is one that has kurtosis greater than a mesokurtic distribution. Leptokurtic distributions are sometimes identified by peaks that are thin and tall. The tails of these distributions, to both the right and the left, are thick and heavy.

Let’s use a hypothetical example of excess positive kurtosis. If you track the closing value ofstockABC every day for a year, you will have a record of how often the stock closed at a given value. If there are a high number of occurrences for just a fewclosing prices, the graph will have a very slender and steep bell-shaped curve.

How do I know if my distribution is platykurtic?

For this reason, a platykurtic distribution will have thinner tails than a normal distribution will, resulting in fewer extreme positive or negative events. The opposite of a platykurtic distribution is a leptokurtic distribution, in which excess kurtosis is positive. The flat tails indicate the small outliers in a distribution. In general, leptokurtic distributions have heavier tails or a higher probability of extreme outlier values when compared to mesokurtic or platykurtic distributions. Whenever the Kurtosis is less than zero or negative, it refers to Platykurtic.

Skewness essentially measures the symmetry of the distribution, while kurtosis determines the heaviness of the distribution tails. These have a greater likelihood of extreme events as compared to a normal distribution. They have a lower likelihood of extreme events compared to a normal distribution. Besides normal distributions, binomial distributions for which p is close to 1/2 are considered to be mesokurtic. There are two possibilities for a distribution is skewed that is ‘positively skewed ‘ and ‘negatively skewed ‘. It is used for selecting the suitable average for analysis of a series.