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| {| class="wikitable" | | {| class="wikitable" |
| |- | | |- |
− | | parameters || <math>s \geq 0\,</math> ([[real number|real]])<br /><math>N \in \{1,2,3\ldots\}</math> ([[integer]]) | + | | 参量|| <math>s \geq 0\,</math> (真实)<br /><math>N \in \{1,2,3\ldots\}</math> (整数) |
| |- | | |- |
− | | support || <math>k \in \{1,2,\ldots,N\}</math> | + | | 支持 || <math>k \in \{1,2,\ldots,N\}</math> |
| |- | | |- |
− | | pdf || <math>\frac{1/k^s}{H_{N,s}}</math> where ''H<sub>N,s</sub>'' is the ''N''th generalized [[harmonic number]] | + | | pmf || <math>\frac{1/k^s}{H_{N,s}}</math> where ''H<sub>N,s</sub>'' is the ''N''th generalized [[harmonic number]] |
| |- | | |- |
− | | cdf || <math>\frac{H_{k,s}}{H_{N,s}}</math> | + | | CDF || <math>\frac{H_{k,s}}{H_{N,s}}</math> |
| |- | | |- |
− | | mean || <math>\frac{H_{N,s-1}}{H_{N,s}}</math> | + | | 意思 || <math>\frac{H_{N,s-1}}{H_{N,s}}</math> |
| |- | | |- |
− | | median || | + | | 模式 || <math>1\,</math> |
| |- | | |- |
− | | mode || <math>1\,</math> | + | | 方差 || <math>\frac{H_{N,s-2}}{H_{N,s}}-\frac{H^2_{N,s-1}}{H^2_{N,s}}</math> |
| |- | | |- |
− | | variance || <math>\frac{H_{N,s-2}}{H_{N,s}}-\frac{H^2_{N,s-1}}{H^2_{N,s}}</math> | + | | MGF || <math>\frac{1}{H_{N,s}}\sum\limits_{n=1}^N \frac{e^{nt}}{n^s}</math> |
| |- | | |- |
− | | mgf || <math>\frac{1}{H_{N,s}}\sum\limits_{n=1}^N \frac{e^{nt}}{n^s}</math> | + | | 碳纤维 || <math>\frac{1}{H_{N,s}}\sum\limits_{n=1}^N \frac{e^{int}}{n^s}</math> |
| |- | | |- |
− | | char || <math>\frac{1}{H_{N,s}}\sum\limits_{n=1}^N \frac{e^{int}}{n^s}</math> | + | | 熵 || <math>\frac{s}{H_{N,s}}\sum\limits_{k=1}^N\frac{\ln(k)}{k^s} |
− | |-
| |
− | | entropy || <math>\frac{s}{H_{N,s}}\sum\limits_{k=1}^N\frac{\ln(k)}{k^s}
| |
| +\ln(H_{N,s})</math> | | +\ln(H_{N,s})</math> |
| |} | | |} |