May, yes, leptokurtic has larger peak but also larger extreme value probabilities. Maybe this is what you overlooked. So, these extreme value will contribute a substantial amount to the total Kurtosis (Sum(density*(x-xmean)^4/sigma^4)) because x is very large for the extreme values. That’s why Leptokurtic has kurtosis>3.
May, yes, leptokurtic has larger peak but also larger extreme value probabilities. Maybe this is what you overlooked. So, these extreme value will contribute a substantial amount to the total Kurtosis (Sum(density*(x-xmean)^4/sigma^4)) because x is very large for the extreme values. That’s why Leptokurtic has kurtosis>3.