Skewness

Characterizing the location and variability of a data collection is a crucial task in many statistical analyses. Skewness and kurtosis are two more characteristics of the data. The skewness distribution is a metric for its symmetry. A distribution’s mode is the highest point in it. The mode denotes the x-axis response value having the highest chance of occurring. If one side of the mode’s tail is fatter or longer than the other, the distribution is skewed: it’s asymmetrical.

Definition of Skewness: –

Asymmetry or distortion of a symmetric distribution is measured by skewness. It calculates the divergence of a random variable’s distribution from a symmetric distribution, such as the normal distribution. Because it is symmetrical on both sides, a normal distribution has no skewness. As a result, if a curve is shifted to the right or left, it is said to be skewed.

In a nutshell, we can say that:

• Skewness is a measure of how far a random variable’s distribution deviates from the symmetrical normal distribution on both sides.
• A distribution can be skewed to the left or right in one of two ways. When a symmetric distribution is applied to skewed data, skewness risk arises.
• Investors examine skewness when evaluating the return distribution of investments since extreme data points are also taken into account.

Types of Skewness:-

Basically there are two types of Skewness there namely; positive skewness and negative skewness. Let us discuss about these briefly:

• Positive Skewness:-

A positively skewed distribution is one in which the tail is on the right side and the body is pushed to the left. The right-skewed distribution is another name for it. The tapering of the curve differently from the data points on the other side is referred to as a tail.

A positively skewed distribution has a skewness value greater than zero, as the name implies. The mean value is bigger than the median and goes towards the right because the skewness of the given distribution is on the right, and the mode occurs at the maximum frequency of the distribution.

• Negative Skewness:-

A negative skewed distribution is one in which the tail is on the left side and the body is pushed to the right. A left-skewed distribution is another name for it. Any distribution with a negative skew has a skewness value that is less than zero. Because the skewness of the given distribution is to the left, the value of mean is less than the value of median and goes to the left, and the mode occurs at the distribution’s highest frequency.

Definition of Kurtosis:-

The kurtosis is another popular shape measurement. Kurtosis is the fourth moment in the distribution, whereas skewness is the third. As a result, outliers in a sample have a greater impact on kurtosis than on skewness, and in a symmetric distribution, both tails raise kurtosis, unlike skewness, where they offset each other. The mean and standard deviation have the same units as the original data, whereas the variance has the square of those units. However, unlike skewness, kurtosis has no units: it’s a single number, similar to a z-score. In relation to a normal distribution, kurtosis is a measure of how heavy-tailed or light-tailed the data are. Heavy tails, or outliers, are more probable in data sets with a high kurtosis. In data sets with low kurtosis, light tails or a lack of outliers are typical. The most extreme instance would be a uniform distribution.

What effect would punching or dragging the normal distribution curve from the top have on the distribution’s shape?

The apex of the curve and the tails of the curve are the two things to note, and the Kurtosis measure is responsible for capturing this occurrence. We’ll adhere to the concept and its visual clarity because the kurtosis calculation method is complicated (4th moment in the moment-based calculation). A mesokurtic distribution has a kurtosis of three and is defined as a normal distribution with a kurtosis of three. Leptokurtic distributions have a number more than three, while platykurtic distributions have a number less than three. As a result, the higher the value, the higher the peakness. Kurtosis is a number that ranges from 1 to infinity. We may calculate extra kurtosis by preserving reference zero for normal distribution because the kurtosis measure for a normal distribution is 3. Excess kurtosis will now range from -infinity to infinity.

Skewness and Kurtosis:-

When you execute a software’s descriptive statistics function, skewness and kurtosis are two typically listed variables. These two statistics, according to several literature, provide insight into the distribution’s form.

The symmetry of a distribution is measured by skewness. The skewness of a symmetrical dataset is 0. As a result, the skewness of a normal distribution is zero. Skewness is a measurement of how big the two tails are in relation to each other.

The combined sizes of the two tails are measured by kurtosis. It calculates how much probability is in the tails. The value is frequently compared to the normal distribution’s kurtosis, which is equal to 3. The dataset has larger tails than a normal distribution if the kurtosis is greater than 3. (more in the tails). The dataset exhibits lighter tails than a normal distribution if the kurtosis is less than 3. (less in the tails). Take care here. “Excess kurtosis” is a term used to describe kurtosis. Subtracting 3 from the kurtosis yields the excess kurtosis. As a result, the kurtosis of the normal distribution is equal to 0.Kurtosis was originally intended to be a metric for determining the peakiness of a distribution. This is a common misunderstanding, despite the fact that it is still included in numerous definitions.

The tails of the distribution are involved in skewness and kurtosis. These are discussed in greater depth further down.

Conclusion:-

A negative skew in an asymmetrical distribution means the tail on the left is longer than the tail on the right (left-skewed), whereas a positive skew means the tail on the right is longer than the tail on the left (right-skewed) (right-skewed). When extreme values cause a distortion in the normal distribution, asymmetric distributions emerge.