@article{oai:mie-u.repo.nii.ac.jp:00005714,
 author = {Matsumiya, Yoshiharu and 松宮, 義晴 and Oka, Masao and 岡, 正雄 and Hiramatsu, Kazuhiko and 平松, 一彦 and Asano, Kenji and 浅野, 謙治},
 journal = {三重大学生物資源学部紀要 = The bulletin of the Faculty of Bioresources, Mie University},
 month = {Jan},
 note = {application/pdf, A simple method which utilizes the fact that the differential coefficients of a parabola give a straight line is proposed for analysing the polymodal length distribution into two or more individual normal distributions. A differential value of ln Yi(=yi, logarithmic frequency of length classes li), dyi/dli can be approximatery given by
dyi/dli = 1/2 ( yi-yi-1/li-li-1+yi+1-yi/li+1-li )
where ln Y = ln 1/2πσ² - (l-m)²/2σ² (for a normal distribution the mean is m and standard deviation σ).  When several straight lines sloping downward to the right can be fitted to the first difference of the logarithmic frequency distribution, the intersections of these straight lines and dy/dl=0 represent mean length of several normal distribution. The method above is applied to the saury and the porgy length distribution., 放射線の微係数が直線になることを利用して, polymodal な体長組成データを複数の正規分布に分解する簡便な方法を提案する。
体長階級liの対数頻度yiの微分値は近似的に
dyi/dli=1/2( yi-yi-1/li-li-1+yi+1-yi/li+1-li )
として表される。ここでY=ln1/2πσ²-(l-m)²/2σ²(平均m, 標準偏差σの正規分布)とする。対数頻度分布の1次階差に幾本かの右さがりの直線をあてはめられた場合, これらの直線と dy/dl=0 との交点が,それぞれの正規分布の平均体長を表現することになる。
上記の方法をサンマとキダイの体長組成の具体例へ適用した。},
 pages = {69--72},
 title = {Analysis of a Mixed Normal Distributioin by Means of the First Difference of the Logarithmic Frequency Distribution},
 volume = {5},
 year = {1991}
}