�� -�� - ��

��

�.�.-�.�. �� (aka Leng)
��
�� 2004
(�� )

� �� (��). �� .

��-��, �� (�� ) �� , � ��.

��-��, �� , � �� - � �� "��". � �� 100% �� , � �� 0% - �� . �� , �� .

�� , �� .

�� - �� , � - �� . �� () �� , �� ��  �� -a �� +a, �� a - �� . �� , � �� . �� D � . �� , �� .

f := proc (x, mu, sigma) options operator, arrow; exp(-1/2*(x-mu)^2/sigma^2)/sqrt(2*Pi*sigma^2) end proc

�� :

D = Int(1/2*exp(-1/2*(x-mu)^2/sigma^2)*2^(1/2)/(Pi*sigma^2)^(1/2),x = mu-a .. mu+a)

�� :

�� - �� . �� - �� . �� , ��

approx := proc (x, t) options operator, arrow; (t^x-1)/(t^x+1) end proc

�� t - ��

��

[Maple Plot]

�� :

D = (t^(a/sigma)-1)/(t^(a/sigma)+1)

�� , �� (��. �� ) - � �� .

�� , �� 0% �� . �� :

D = (t^(a/sigma)-t^(a/sigma[max]))/(t^(a/sigma)+t^(a/sigma[max]))

�� a.

�� , �� , �� sigma = sigma[max]/2 �� 50%.

�� a = ln(3)*sigma[max]/ln(t)

�� :

D = (3^(sigma[max]/sigma)-3)/(3^(sigma[max]/sigma)+3)