example (censored datasuppose the lifetime (in yearsof certain type of machine is modeled via (us distribution to estimate and the lifetimes of (independentmachines are recorded up to years denote these censored lifetimes by xn the {xi are thus realizations of iid random variables {xi }distributed as min{yc}where (us by the law of total probability (see ( ))the marginal pdf of each can be written asphs ( { cph(( )/ { } ( us ph(( )/ { { ph(( )/sp[ >cp[ <cwhere phs (*is the pdf of the ( distributionph is the cdf of the standard normal distributionand ph : ph it follows that the likelihood of the data { xn as function of the parameter th :[us ]is- ) exp ( ( thx ph(( )/ ps :xi < :xi = let nc be the total number of xi such that xi using nc latent variables [ znc ]we can write the joint pdfpnc :xi < (xi ui= (zi uexp min (tz thi ( ps ) / so that (tz thdz ( thwe can thus apply the em algorithm to maximize the likelihoodas follows for the (xpectation)-stepwe have for fixed thg( tthnc = (zi tth)where ( tth { cphs ( )/ph(( )/sis simply the pdf of the (us distributiontruncated to [cfor the (aximization)-stepwe compute the expectation of the complete loglikelihood with respect to fixed ( tthand use the fact that znc are iidp nc ( ) :xi < (xi uln ln( ) ln (tz th where has (us distributiontruncated to [cto maximize the last expression with respect to we set the derivative with respect to to zeroand obtainp nc ez :xi < xi un similarlysetting the derivative with respect to to zero givesp nc ( ) :xi < (xi ) in summarythe em iterates for are as follows