What is the formula calculating kurtosis?

What is the formula calculating kurtosis?

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 * Σni(Yi – Ȳ)4 / (Σni(Yi – Ȳ)2)2.

What is histogram kurtosis?

Kurtosis is a measure of the combined weight of a distribution’s tails relative to the center of the distribution. When a set of approximately normal data is graphed via a histogram, it shows a bell peak and most data within three standard deviations (plus or minus) of the mean.

How do you find kurtosis in R?

Base R does not contain a function that will allow you to calculate kurtosis in R. We will need to use the package “moments” to get the required function. The kurtosis measure describes the tail of a distribution – how similar are the outlying values of the distribution to the standard normal distribution?

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. A uniform distribution would be the extreme case.

What is kurtosis R?

The excess kurtosis of a univariate population is defined by the following formula, where μ2 and μ4 are respectively the second and fourth central moments. Intuitively, the excess kurtosis describes the tail shape of the data distribution.

What is a Mesokurtic?

Mesokurtic is a statistical term used to describe the outlier characteristic of a probability distribution in which extreme events (or data that are rare) is close to zero. A mesokurtic distribution has a similar extreme value character as a normal distribution.

What is Mesokurtic kurtosis?

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. In contrast, a leptokurtic distribution has fatter tails.

What is the formula for kurtosis?

Kurtosis = n * Σ n i (Y i – Ȳ) 4 / (Σ n i (Y i – Ȳ) 2) 2. Relevance and Use of Kurtosis Formula. For a data analyst or statistician, the concept of kurtosis is very important as it indicates how are the outliers distributed across the distribution in comparison to a normal distribution.

What is the moment coefficient of kurtosis?

The moment coefficient of kurtosis (also known as Pearson’s moment coefficient of kurtosis) is denoted by and is defined as If or , then the data is leptokurtic.

How do you calculate the relative kurtosis of distribution?

At times, relative kurtosis of distribution is represented in terms of excess kurtosis wherein it is calculated by deducting 3 from the kurtosis, i.e. (kurtosis – 3)

What is the kurtosis of frequency curve?

Kurtosis is the peakedness of a frequency curve. Even if two curves have the same average, dispersion and skewness, one may have higher (or lower) concentration of values near the mode, and in this case, its frequency curve will show a sharper peak (or flatter peak) than the other.