Answer: Excess kurtosis is a measure relative to the uniform distribution, which has a kurtosis of 3

## Explanation Kurtosis measures the peakedness of a distribution and the heaviness of its tails. The key concepts are: 1. **Kurtosis of Normal Distribution**: The normal distribution has a kurtosis of exactly 3. 2. **Excess Kurtosis**: This is defined as kurtosis minus 3 (the kurtosis of the normal distribution). Therefore, excess kurtosis is measured relative to the **normal distribution**, not the uniform distribution. 3. **Types of Distributions**: - **Leptokurtic**: Excess kurtosis > 0 (positive) - distribution has fatter tails and higher peak than normal - **Platykurtic**: Excess kurtosis < 0 (negative) - distribution has thinner tails and flatter peak than normal - **Mesokurtic**: Excess kurtosis = 0 - distribution has same kurtosis as normal **Why Option A is incorrect**: - Excess kurtosis is measured relative to the **normal distribution** (kurtosis = 3), not the uniform distribution. - The uniform distribution actually has a kurtosis of 1.8, not 3. **Correct statements**: - Option B: Correct - Negative excess kurtosis indicates platykurtic distribution - Option C: Correct - Positive excess kurtosis indicates leptokurtic distribution - Option D: Correct - Normal distribution has kurtosis equal to 3 This question tests understanding of kurtosis measurement and the reference point for excess kurtosis calculations.

Author: Nikitesh Somanthe