Pm

As a preliminary coefficient c'(ay b) we will assume the number the number of points of the set vir(D)

the total number of points in the set vir(D) '

It is clear that number c'(a,b) is the integral of density function z(x) along the parallelepiped P'(a, b).

The meaning of this preliminary coefficient c'(ayb) is clear. It is natural to call dynasties, or vectors of vir(D)y falling into parallelepiped P'(ay b), "similar" to dynasties a and b. In fact, each of such dynasties is located no further from dynasty a than dynasty b is located from dynasty a. Consequently, as a measure of proximity of two dynasties a and by we take the part of dynasties "similar" to a and b in the set of all dynasties vir(D).

However, such coefficient c'(a, b) is not sufficiently good yet, since it does not consider the circumstance that the chroniclers could determine certain reign durations with a certain error, - the longer the rule, the larger the error. In other words, we have to take into account the error of chroniclers (3) discussed above.

Let us switch to the simulation of error (3). Let T be duration of a reign. It is clear that the duration of rule maybe considered a random variable determined for "the set of all kings". Let us designate the number of kings ruling for T years as g(T). In the paper [884] the author of the present book experimentally calculated this frequency histogram g(T) (density of distribution of the indicated random value) on the basis given in Chronological Tables by J. Blair ( [76]). Let us assume h(T) = l/g(T) and call h(T) a function of the chroniclers' errors. The lower the probability that a random variable, or the duration of reign, assumes the value of T, the greater the error h(T) in the determi-

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