What is Kurtosis?
What does kurtosis mean?
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.
What is a kurtosis in statistics?
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 kurtosis tells us?
Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. In other words, kurtosis identifies whether the tails of a given distribution contain extreme values.
What is kurtosis with example?
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. There are three types of kurtosis: mesokurtic, leptokurtic, and platykurtic.
What is the difference between kurtosis and skewness?
Skewness is a measure of the degree of lopsidedness in the frequency distribution. Conversely, kurtosis is a measure of degree of tailedness in the frequency distribution. Skewness is an indicator of lack of symmetry, i.e. both left and right sides of the curve are unequal, with respect to the central point.
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.
Can kurtosis be negative?
The values of excess kurtosis can be either negative or positive. When the value of an excess kurtosis is negative, the distribution is called platykurtic. This kind of distribution has a tail that’s thinner than a normal distribution.
How do you find kurtosis in statistics?
Kurtosis = Fourth Moment / Second Moment2
- Kurtosis = 313209 / (365)2
- Kurtosis = 2.35.
What is acceptable skewness and kurtosis?
Both skew and kurtosis can be analyzed through descriptive statistics. Acceptable values of skewness fall between ? 3 and + 3, and kurtosis is appropriate from a range of ? 10 to + 10 when utilizing SEM (Brown, 2006).
What is the importance of kurtosis?
Applications. The sample kurtosis is a useful measure of whether there is a problem with outliers in a data set. Larger kurtosis indicates a more serious outlier problem, and may lead the researcher to choose alternative statistical methods.
Is high kurtosis good or bad?
Kurtosis is only useful when used in conjunction with standard deviation. It is possible that an investment might have a high kurtosis (bad), but the overall standard deviation is low (good). Conversely, one might see an investment with a low kurtosis (good), but the overall standard deviation is high (bad).
What does negative kurtosis tell us?
A distribution with a negative kurtosis value indicates that the distribution has lighter tails than the normal distribution. For example, data that follow a beta distribution with first and second shape parameters equal to 2 have a negative kurtosis value.
Why is kurtosis 3?
This heaviness or lightness in the tails usually means that your data looks flatter (or less flat) compared to the normal distribution. 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. These distributions are called mesokurtic.
Why do we use 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.
How do you interpret kurtosis value?
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 do you calculate kurtosis in Excel?
What is high kurtosis?
High kurtosis in a data set is an indicator that data has heavy tails or outliers. If there is a high kurtosis, then, we need to investigate why do we have so many outliers. It indicates a lot of things, maybe wrong data entry or other things.
What is flat a quartic?
Description. McBryde-Thomas flat-polar quartic is an equal-area pseudocylindrical projection. The projection is based on the quartic authalic projection. Its boundary meridians bulge outward excessively, producing considerable shape distortion near the map outline.
What is a Leptokurtic distribution?
Leptokurtic distributions are variable distributions with wide tails and have positive kurtosis. In contrast, platykurtic distributions have narrow tails and thus have negative kurtosis, whereas mesokurtic distributions (such as the normal distribution) have a kurtosis of zero.
How do you interpret skewness and kurtosis in Minitab?
What does a skewness of 0.05 mean?
As a general rule of thumb: If skewness is less than -1 or greater than 1, the distribution is highly skewed. If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed. If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.
What is the range of kurtosis?
Kurtosis can reach values from 1 to positive infinite. A distribution that is more peaked and has fatter tails than normal distribution has kurtosis value greater than 3 (the higher kurtosis, the more peaked and fatter tails).
Which kurtosis has fat tails?
Leptokurtic distributions are statistical distributions with kurtosis greater than three. It can be described as having a wider or flatter shape with fatter tails resulting in a greater chance of extreme positive or negative events.
Does kurtosis affect standard deviation?
The higher the standard deviation, the more spread out the data is, while the lower the kurtosis the more spread out the data is.
What does a skewness of 0.5 mean?
A skewness value greater than 1 or less than -1 indicates a highly skewed distribution. A value between 0.5 and 1 or -0.5 and -1 is moderately skewed. A value between -0.5 and 0.5 indicates that the distribution is fairly symmetrical.