The Nested EM Algorithm for the Parameters of the Exponential-Geometric Model
Yanlin Wang · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2014
In this article we introduce the exponential geometric distribution( EG for brevity) as a model,which is obtained by mixing the exponential distribution with one truncated geometric distribution. It has the density of f( x; β,p) = β( 1-p) × e-2βx( 2-pe-βx)(1-pe-βx)-2. By straightforward integration we find that the various moments of the EG is E( xr; β,p) =p-1(1-p) r! β-r p-1[L( p,r)-1]. Firstly,we discuss that the maximum likelihood estimates of β and p can not be get in explicit solution form; it should be solved by numerical algorithm. Then we nest one EM algorithm within the outer EM algorithm to solve the problem. Note that,for the outer EM algorithm the missing data are based on the mixture representation while at the inner EM algorithm,the missing data are the truncated observations. In the end we get the maximum likelihood estimators of parameters.