The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data

Abstract

This paper is concerned with the nonparametric estimation of a distribution function F, when the data are incomplete due to grouping, censoring and/or truncation. The situation occurs frequently in survivorship, reliability, and recidivism analysis. Using the idea of self-consistency, a simple algorithm is constructed and shown to converge monotonically to yield a maximum likelihood estimate of F. The procedure compares favourably with the more cumbersome Newton-Raphson method. A test is proposed for comparing two distributions when data on one or both is incomplete and some other applications of the empirical distribution function are indicated.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1976
Accession Number
ADA030940

Entities

People

  • Bruce W. Turnbull

Organizations

  • Cornell University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Asymptotic Normality
  • Consistency
  • Convergence
  • Data Science
  • Distribution Functions
  • Engineering
  • Equations
  • Information Science
  • Maximum Likelihood Estimation
  • Military Research
  • Operations Research
  • Order Statistics
  • Probability
  • Random Variables
  • Rank Order Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Statistical inference.