The prefix exchange distance of a permutation is the length its shortest factorisation into transpositions that all contain 1. Using probabilistic approach, we obtain expressions for mean and variance, prove asymptotic normality distribution this random verifying Ewens sampling formula. Analogous results in uniform setting follow as simple corollaries.

introduction: present children are the investments of community in the future. preparing children health which leads to the stability of community health, provided to accurate implementation of educational and health programs in the community and especially in mothers. so it is necessary to determine the relationship between parents' literacy with growth rate in children.   materials and m...

with the entry of god and spirituality into areas of organization and management, as the challenge of the twenty-first century, managers and leaders of organizations, especially educational institutions must deal with new phenomena. therefore the purpose of the present study was to investigate the relationship between spirituality leadership and organizational entrepreneurship from view point o...

We study random circle graphs which are generated by throwing n points (vertices) on the circle of unit circumference at random and joining them by an edge if the length of shorter arc between them is less than or equal to a given parameter d. We derive here some exact and asymptotic results on sizes (the numbers of vertices) of ”typical” connected components for different ways of sampling them...

The purpose of this paper is to find the estimate of the parameters of k and g   distribution for ranked set sample by numerically maximizing the likelihood function. The estimates named as numerical maximum likelihood estimate, and corresponding mean square error and relative efficiency compared to simple random sampling are computed using a computer simulation. Ranked set sampling is seen t...