What is the meaning of the word kurtosis?

What is the meaning of the word kurtosis?

Definition of kurtosis : the peakedness or flatness of the graph of a frequency distribution especially with respect to the concentration of values near the mean as compared with the normal distribution.

What is kurtosis example?

The kurtosis of any univariate normal distribution is 3. 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.

What is measure of kurtosis?

In statistics, a measure of kurtosis is a measure of the “tailedness” of the probability distribution of a real-valued random variable. The standard measure of kurtosis is based on a scaled version of the fourth moment of the data or population. A distribution having a relatively high peak is called leptokurtic.

What is Mesokurtic curve?

Mesokurtic distributions have a kurtosis of zero, meaning that the probability of extreme, rare, or outlier data is close to zero. Mesokurtic distributions have the same kurtosis as that of the normal distribution, or normal curve, also known as a bell curve.

What is kurtosis of normal distribution?

A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. An increased kurtosis (>3) can be visualized as a thin “bell” with a high peak whereas a decreased kurtosis corresponds to a broadening of the peak and “thickening” of the tails.

What does a kurtosis of 3 mean?

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).

What is skewness and kurtosis?

Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.

What is kurtosis and skewness?

Skewness is a measure of symmetry, or more precisely, the lack of symmetry. 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.

Why kurtosis of normal distribution is 3?

The sample kurtosis is correspondingly related to the mean fourth power of a standardized set of sample values (in some cases it is scaled by a factor that goes to 1 in large samples). As you note, this fourth standardized moment is 3 in the case of a normal random variable.

What does it mean when kurtosis is zero?

What does it mean when kurtosis is zero? When kurtosis is equal to 0, the distribution is platykurtic. 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.

What is a kurtosis in statistics?

Kurtosis is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. The peak is the tallest part of the distribution, and the tails are the ends of the distribution.

What is the difference between kurtosis and skewness?

DEFINITION of ‘Kurtosis’. Whereas skewness differentiates extreme values in one versus the other tail, kurtosis measures extreme values in either tail. Distributions with large kurtosis exhibit tail data exceeding the tails of the normal distribution (e.g., five or more standard deviations from the mean).

What is the difference between kurtosis and mesokurtic distribution?

Kurtosis is typically measured with respect to the normal distribution. A distribution that has tails shaped in roughly the same way as any normal distribution, not just the standard normal distribution, is said to be mesokurtic.

Does kurtosis measure peak or tailedness?

However, kurtosis is a measure that describes the shape of a distribution’s tails in relation to its overall shape. A distribution can be infinitely peaked with low kurtosis, and a distribution can be perfectly flat-topped with infinite kurtosis. Thus, kurtosis measures “tailedness,” not “peakedness.”