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.