Mode Calculation Method of Agricultural Production Indices Based on Lp-Norm Estimation

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  • Lpノルム推定による農業生産指標の最頻値計算法
  • Lp ノルム スイテイ ニ ヨル ノウギョウ セイサン シヒョウ ノ サイヒンチ ケイサンホウ

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Abstract

<p> Existing research on agricultural production management has not addressed the problem of selecting representative values of agricultural production indices. For agricultural production indices such as working hours per unit area and yield per unit area of crop production, there are cases wherein it is desirable to obtain typical values as representative values. This is because production indices tend to have long-tail distribution on one side in agriculture that is susceptible to the natural environment. In this research, we focused on the mode, which is a representative value with typicality of the agricultural production indices. However, a mode calculation method that can sufficiently withstand practical use has not yet been established. Usually, the mode is obtained as a class value of the maximum class after creating a histogram. However, even if the class width is kept constant, the mode obtained by the usual method is indefinite depending on how to determine the "anchor position" and uniqueness is not guaranteed. It is not desirable to use the most frequent value obtained by the usual method as the representative value of the production indices. Therefore, we selected Lp-norm estimation when the degree p is a positive decimal real number close to 0 as the mode calculation method without using histogram. However, computation of the Lp-norm estimator whose degree p is less than 1 is a nonlinear, non-convex problem, and so it is not easy to solve the global optimal solution strictly. In this study, we presented a simple calculation method for a non-convex problem using worksheets of spreadsheet software for calculating the unique mode through Lp-norm estimation including degree p less than 1, and we tried to apply the method to the mode of actual agricultural production indices. </p>

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