情報関数が最大エントロピー分布に及ぼす影響の解析 ; Analysis of Effect of Information Function on Maximum Entropy Distribution

The effects of 4 information functions on a 1-variable maximum entropy distribution (1MED) were analyzed using simulation data from 6 assumed populations and annual maximum daily rainfall data. For this study, 6 gamma distributions with different parameters were taken as the populations and xr, 1/xr, (lnx)r and exp(- rx/ M) (M=E[X]) functions were adopted as the four information functions. The calculation results using simulation date from the 6 gamma distributions could not fit the 1MED (obtained from information functions with r=1,2) to the population satisfactorily. The combined information of xm and exp(-nx/M), or (m, n) -information, improved the fitness of the 1MED to the population in both the shape of the p. d. f. and the return period of the right tail. Furthermore, it was found that the (1,2), (1,3) and (1,4)-informations are particularly suitable for steep shaped populations having peaks in the left side, while the (1,2), (1,3), (2,3) and (2,4)-informations are best for flat form populations exhibiting peak shifts to the lower right. These 5 types of 1MEDs gave the most stable and realistic return periods for annual maximum daily rainfalls measured in the Nagano prefecture. ; Article ; 信州大学工学部紀要 70: 21-31 (1992) ; departmental bulletin paper