• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.391-401
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• 2011

Consider a cluster, so called a 'son cluster', whose mean and variance is composed of the means and variances of both clusters called as a 'father cluster' and a 'mother cluster'. In this paper, a method for identifying each of three clusters is provided by modeling the relationship with father and mother clusters. Under the normal mixture model, the parameters are estimated via EM algorithm. We were able to overcome the problems of estimation using ECM approximation. Numerical examples show that our method can effectively identify the three clusters, so called a 'family of clusters'.