Skewness and Kurtosis[1].pptx

Skewness and Kurtosis

1. Skewness and Kurtosis

2. Skewness Skewness essentially is a commonly used measure in descriptive statistics that characterizes the asymmetry of a data distribution. It provides information about the shape of the distribution and the extent to which it deviates from symmetry. In a symmetrical distribution, the values are evenly distributed around the mean, resulting in a skewness value of zero. in an asymmetric distribution, the values tend to be concentrated on one side of the mean, causing the distribution to be skewed.

3. Skewness can help identify whether the tail of the distribution is elongated to the left (negative skewness ) or to the right (positive skewness ). Positive skewness (right-skewed distribution): In a positively skewed distribution, the tail on the right side of the distribution is longer or stretched out compared to the left side. This means that the majority of the data points are concentrated towards the lower values, and there are a few extreme high values. Negative skewness (left-skewed distribution): In a negatively skewed distribution, the tail on the left side of the distribution is longer or stretched out compared to the right side. This means that the majority of the data points are concentrated towards the higher values, and there are a few extreme low values.

4. Positive Skewness Negative Skewness

5. Skewness Coefficient Skewness can be calculated using various methods, whereas the most commonly used method is Pearson’s coefficient. Pearson’s coefficient of skewness :

6. Kurtosis Kurtosis is a statistical measure that describes the shape and peakedness of a probability distribution. It provides information about the tails of the distribution and the presence of outliers. Kurtosis measures the degree to which the distribution of a variable deviates from a normal distribution (also known as the Gaussian distribution or bell curve). A normal distribution has a kurtosis value of 0.

7. Positive kurtosis (leptokurtic distribution) : A positively kurtotic distribution has heavier tails and a higher peak compared to a normal distribution. It indicates that the data has more extreme values or outliers than would be expected in a normal distribution. This means that there is a higher probability of extreme values occurring. Negative kurtosis ( platykurtic distribution) : A negatively kurtotic distribution has lighter tails and a flatter peak compared to a normal distribution. It indicates that the data has fewer extreme values or outliers than would be expected in a normal distribution. This means that extreme values are less likely to occur. Excess kurtosis : Kurtosis is often reported as excess kurtosis, which is the kurtosis value minus 3. This adjustment allows the normal distribution to have an excess kurtosis value of 0.

8. Types of Excess Kurtosis Leptokurtic or heavy-tailed distribution (kurtosis more than normal distribution) Mesokurtic (kurtosis same as the normal distribution) Platykurtic or short-tailed distribution (kurtosis less than normal distribution) Leptokurtic (Kurtosis > 3) Platykurtic (Kurtosis < 3) Mesokurtic (Kurtosis = 3)