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本文提出了逻辑斯谛曲线的一种新的K值估算方法——四点式平均值法。利用在时间序列t_0,t_1,t_2,…t_n内所得的n+1个观察值中具有相同的时间间距的两对点t_i,t_i,t_k,t_1(t_1-t_k=t_i-ti=△t,k≠i)所得的4个观察值,可对逻辑斯谛方程的上界K值进行估算。在全序列中举尽能满足此一条件的所有数组,求得多个K的估算值,取数学期望作为K的无偏估计值。 本法较以往的目测法、三点法和平均值法为好,但所得结果可能稍逊于枚举选优法,但是,四点式平均值法可以应用于非自然数离散型分布、K值很大或可能出现的范围较大、以及在种群未达平衡时便终止试验等类型的数据。在这些情况下,枚举选优法的应用则受到一定的限制。
In this paper, we propose a new K value estimation method of logistic curve - four-point average method. Using two pairs of points t_i, t_i, t_k, t_1 (t_1-t_k = t_i-ti = Δt) having the same time interval among the n + 1 observation values obtained in the time series t_0, t_1, t_2, k ≠ i) The resulting four observations allow the estimation of the upper bound K of the logistic equation. In the full sequence, take all the arrays that can satisfy this condition, find the estimates of multiple K, and take mathematical expectation as the unbiased estimate of K. This method is better than the previous visual method, three-point method and average method, but the result may be slightly less than the enumeration and preference method, however, the four-point average method can be applied to the discrete distribution of non-natural number, K value Large or likely to occur in large areas, as well as in the population is not balanced when the test and other types of data. Under these circumstances, the application of enumeration and preference method is limited.