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15.3.3 The K mixture

• negative binomial $BDxEY$K$h$/(B fit $B$9$k(B simple $B$J(B distribution model
  
  $$\begin{eqnarray*}P_i(k) &=& (1-\alpha)\delta_{k,0} + \frac{\alpha}{\beta+1} \Bigl(\frac{\beta}{\beta+1}\Bigr)^k \\ \end{eqnarray*}$$
  
  
  
  $$\begin{eqnarray*}\left\{ \begin{array}{rll} \lambda_i&=& \frac{cf_i}{N} \\ I... ...lpha &=& \frac{\lambda_i}{\beta} \end{array} \right. \nonumber \end{eqnarray*}$$
  
  
• df_i $B$O(B $B$=$l$>$l$N(B document $B$G(B w_i$B$,:GDc(B 1$B2s$:$D=P8=$7$?$H(B $B2>Dj$7$?>l9g$N(Btotal$B$N=P8=2s?t(B, $Bcf_i$B$@$+$i(B cf_i-df_i $B$O:GDc(B 1$B2s$:(B $B$D$H$OJL$K(B, $BM>$C$F=P8=$7$?2s?t$H$J$k(B
• $\beta$ $\rightarrow$ $B3F(B document $B$K$O:GDc(B 1$B8D(B $B$H$O(B $BJL$K(B, $B$"$U$l$F(B $\beta$ $B8D(B w_i $B$,=P8=$9$k(B
• $\frac{\beta}{\beta+1}$ $\rightarrow$ $BA4IQEY$KBP$9$7$F(B, $BM>$C$F=P8=$7$?IQEY$N3d9g(B
  
  $$\begin{eqnarray*}1 &\rightarrow& \Bigl(\frac{\beta}{\beta+1}\Bigr)^1\\ 2 &\rig... ...ts& \\ n &\rightarrow& \Bigl(\frac{\beta}{\beta+1}\Bigr)^n\\ \end{eqnarray*}$$
  
  
• $BNc(B Table 15.7
  • K mixture $B$O(B non-content word $B$NJ,I[$r6a;w$9$k$N$KFC$KM%$l$F$$$k(B
  • content word $B$G$O(B $\frac{P_i(k)}{P_i(K+1)} = const$ $B$,J]$?(B $B$l$J$$(B,$B8:>/798~(B (soviet $B$NNc(B)
  • $B$=$N(B document $B$N(B core topic $B$K4XO"$9$kC18l$O=8Cf$7$F(B $BJ,I[$7$d$9$$(B, $B=P8=IQEY$,B?$$C18l$O(B central concept $B$r(B $BI=8=$7$F$k2DG=@-$,9b$$(B