# Zero-Inflated Patent Data Analysis Using Compound Poisson Models
## 4 Experimental Results
### Patent Data Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Keyword** & **Min** & **Q1** & **Median** & **Q3** & **Max** & **Mean** & **Percentage of Zero Values** \\ \hline drone & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 28 & 0.1750 & 0.9518 \\ control & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 33 & 1.4280 & 0.5806 \\ device & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 24 & 0.9813 & 0.6546 \\ flight & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 27 & 0.7134 & 0.7259 \\ aircraft & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 26 & 0.6868 & 0.7748 \\ wing & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 34 & 0.4832 & 0.8810 \\ power & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 26 & 0.4548 & 0.8254 \\ data & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 22 & 0.4104 & 0.8610 \\ rotate & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 24 & 0.3800 & 0.8432 \\ motor & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 19 & 0.3727 & 0.8650 \\ drive & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 22 & 0.2996 & 0.8742 \\ camera & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 27 & 0.2807 & 0.8928 \\ signal & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 21 & 0.2724 & 0.8973 \\ detect & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 25 & 0.2619 & 0.8913 \\ battery & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 26 & 0.2320 & 0.9284 \\ sensor & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 16 & 0.2266 & 0.9069 \\ shaft & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 20 & 0.2160 & 0.9158 \\ propel & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 24 & 0.2072 & 0.9229 \\ automat & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 17 & 0.1669 & 0.9049 \\ charge & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 28 & 0.1625 & 0.9606 \\ remote & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 21 & 0.1512 & 0.9274 \\ \hline \end{tabular}
\end{table} 
Table 4: Summary statistics of patent data. \begin{table}
\begin{tabular}{c c c c c} \hline
**Explanatory Variable** & **LM** & **GLM** & **ZIP** & **CP** \\ \hline control & \(-\)0.0047 (0.0106) & \(-\)0.0242 (0.0001) & 0.0495 (0.0001) & \(-\)0.0259 (0.0509) \\ device & \(-\)0.0076 (0.0005) & \(-\)0.0503 (0.0001) & \(-\)0.0355 (0.0001) & \(-\)0.0565 (0.0007) \\ flight & \(-\)0.0023 (0.3590) & \(-\)0.0118 (0.0590) & 0.0417 (0.0001) & \(-\)0.0181 (0.3271) \\ aircraft & \(-\)0.0262 (0.0001) & \(-\)0.4066 (0.0001) & \(-\)0.0776 (0.0001) & \(-\)0.2913 (0.0001) \\ wing & \(-\)0.0096 (0.0001) & \(-\)1.1221 (0.0001) & \(-\)0.0178 (0.1172) & \(-\)0.0991 (0.0001) \\ power & \(-\)0.0122 (0.0001) & \(-\)0.1155 (0.0001) & 0.0107 (0.3166) & \(-\)0.0887 (0.0011) \\ data & 0.0153 (0.0001) & \(-\)0.0528 (0.0001) & 0.0011 (0.8683) & 0.0592 (0.0007) \\ rotate & \(-\)0.0133 (0.0003) & \(-\)0.1484 (0.0001) & 0.0160 (0.3388) & \(-\)0.1455 (0.0002) \\ motor & \(-\)0.0166 (0.0001) & \(-\)0.1615 (0.0001) & \(-\)0.0513 (0.0044) & \(-\)0.1289 (0.0002) \\ drive & \(-\)0.0128 (0.0013) & \(-\)0.1493 (0.0001) & \(-\)0.0515 (0.0017) & \(-\)0.0751 (0.0463) \\ camera & \(-\)0.0054 (0.1530) & \(-\)0.0326 (0.0007) & \(-\)0.0031 (0.7927) & \(-\)0.0277 (0.3116) \\ signal & 0.0154 (0.0001) & 0.0632 (0.0001) & 0.0047 (0.5774) & 0.0816 (0.0002) \\ detect & \(-\)0.0047 (0.2488) & \(-\)0.0313 (0.0015) & \(-\)0.0184 (0.1340) & \(-\)0.0168 (0.5493) \\ battery & \(-\)0.0139 (0.0001) & \(-\)0.1312 (0.0001) & \(-\)0.0220 (0.1689) & \(-\)0.1398 (0.0001) \\ sensor & 0.0121 (0.0085) & 0.0540 (0.0001) & 0.0543 (0.0001) & 0.0654 (0.0165) \\ \hline \end{tabular}
\end{table} 
Table 5: Analysis results of comparative models using patent data. In Table 5, the linear regression model is defined as (9):  
\[\textit{drone}=\beta_{0}+\beta_{1}\textit{control}+\cdots+\beta_{20}\textit{ prenot}+\varepsilon \tag{14}\]  
where \((\beta_{0},\beta_{1},\ldots,\beta_{20})\) are regression coefficients and \(\varepsilon\) is the error term distributed to Gaussian with zero mean and equal variance. We compared the analysis results between CP and the other models according to model coefficient, its \(p\)-value and AIC. In Table 5, we knew that the AIC value of CP is smaller than the comparative models, LM, GLM and ZIP. This means that the model explanatory power of CP is greater than the other models.