Write short note:
(a) Skewness vs. coefficient-of skewness
(b) Leptokurtic vs. Platykurtic kurtosis
(c) Positive skewness and Negative skewness
Answers
(a) : There are several ways to measure skewness. Pearson's first and second coefficients of skewness are two common ones. Pearson's first coefficient of skewness, or Pearson mode skewness, subtracts the mode from the mean and divides the difference by the standard deviation.
(b) : Leptokurtic: More values in the distribution tails and more values close to the mean (i.e. sharply peaked with heavy tails)
Platykurtic: Fewer values in the tails and fewer values close to the mean (i.e. the curve has a flat peak and has more dispersed scores with lighter tails).
leptokurtic distributions have a relatively high probability of extreme events, whereas the opposite is true for platykurtic distributions.
(C) : The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution, negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right.
Negative skew refers to a longer or fatter tail on the left side of the distribution, while positive skew refers to a longer or fatter tail on the right.