Order r	Moment $M_{0} (r)$	Central Moment: $M_{μ} (r)$
1	$e^{m + \frac{1}{2} s^{2}}$	0
2	$e^{2 m + 2 s^{2}}$	$e^{2 m} (e^{2 s^{2}} - e^{s^{2}})$
3	$e^{3 m + \frac{9}{2} s^{2}}$	$e^{3 m} (e^{\frac{9}{2} s^{2}} - 3 e^{\frac{5}{2} s^{2}} + 2 e^{\frac{3}{2} s^{2}})$
4	$e^{4 m + 8 s^{2}}$	$e^{4 m} (e^{8 s^{2}} - 4 e^{5 s^{2}} + 6 e^{3 s^{2}} - 3 e^{2 s^{2}})$
5	$e^{5 m + \frac{25}{2} s^{2}}$	$e^{5 m} (e^{\frac{25}{2} s^{2}} - 5 e^{\frac{17}{2} s^{2}} + 10 e^{\frac{11}{2} s^{2}} - 10 e^{\frac{7}{2} s^{2}} + 4 e^{\frac{5}{2} s^{2}})$
6	$e^{6 m + 18 s^{2}}$	$e^{6 m} (e^{18 s^{2}} - 6 e^{13 s^{2}} + 15 e^{9 s^{2}} - 20 e^{6 s^{2}} + 15 e^{4 s^{2}} - 5 e^{3 s^{2}})$
7	$e^{7 m + \frac{49}{2} s^{2}}$	$e^{7 m} (e^{\frac{49}{2} s^{2}} - 7 e^{\frac{37}{2} s^{2}} + 21 e^{\frac{27}{2} s^{2}} - 35 e^{\frac{19}{2} s^{2}} + 35 e^{\frac{13}{2} s^{2}} - 21 e^{\frac{9}{2} s^{2}} + 6 e^{\frac{7}{2} s^{2}})$
8	$e^{8 m + 32 s^{2}}$	$e^{8 m} (e^{32 s^{2}} - 8 e^{25 s^{2}} + 28 e^{19 s^{2}} - 56 e^{14 s^{2}} + 70 e^{10 s^{2}} - 56 e^{7 s^{2}} + 28 e^{5 s^{2}} - 7 e^{4 s^{2}})$
Statistic	Symbol	Expression
Standard Deviation	$σ$	$e^{m} \sqrt{(e^{2 s^{2}} - e^{s^{2}})}$
Skewness	Sk	$(e^{3 s^{2}} - 3 e^{s^{2}} + 2) / {(e^{s^{2}} - 1)}^{\frac{3}{2}}$
Kurtosis	K	$e^{4 s^{2}} + 2 e^{3 s^{2}} + 3 e^{2 s^{2}} - 3$
Variance of Skewness	Var (Sk)	$\frac{V a r (M_{μ} (3))}{S^{6}} + \frac{3 M_{μ} {(3)}^{2} V a r (M_{μ} (2))}{4 S^{13}}$
Variance of Kurtosis	Var (K)	$\frac{V a r (M_{μ} (4))}{S^{8}} + \frac{2 M_{μ} {(4)}^{2} V a r (M_{μ} (2))}{S^{16}}$