## Technical Report, Issue 305The School, 1976 - Operations research |

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### Contents

Reduction of the problem | 5 |

The selfconsistency algorithm ll | 11 |

The equivalence and convergence theorem | 15 |

3 other sections not shown

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### Common terms and phrases

aikSk arbitrary censoring Army Research Office Asano assume censoring and truncation converge monotonically cumbersome Newton-Raphson data are incomplete defined disjoint intervals distributions when data double censoring Turnbull Efron EMPIRICAL DISTRIBUTION FUNCTION equivalence class estimate F estimate of F exact observations example function F grouped data hazard rate i.e. the largest i'th observation i=l j=l idea of self-consistency incomplete due independent observations iterative procedure large sample properties largest observation left censored left truncation Lehmann alternatives Lemma likelihood function line are given LOGRANK TEST Mantel l967 maximises 2.2 maximum likelihood estimate MLE of F MLE's monotonically to yield multinomial distribution Newton-Raphson method nonparametric estimation observation is censored observed exactly obtaining partition Peto random random variable real line REPORT NUMBER right censored data sample test Section self-consistency algorithm self-consistent estimates shown to converge simple algorithm single censoring singly censored data Subsets test statistic truncated data truncated distribution Unclassified vector x-values