For a distribution, the mean is 10, variance is 16, γ 1is + 1 and β 2is 4. The distribution is:
leptokurtic
The shape of a distribution's tails is described by kurtosis, measured by \(\beta_2\). The benchmark is the normal distribution, for which \(\beta_2 = 3\) (mesokurtic).
Classification rule:
\[\beta_2 > 3 \Rightarrow \text{leptokurtic},\quad \beta_2 = 3 \Rightarrow \text{mesokurtic},\quad \beta_2 < 3 \Rightarrow \text{platykurtic}\]
Here \(\beta_2 = 4 > 3\), so the distribution is more peaked with heavier tails than normal. The skewness value \(\gamma_1 = +1\) only indicates positive asymmetry and does not affect the kurtosis label. Hence the distribution is leptokurtic.
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