Truncated Sequential Hypothesis Tests

Abstract

Through a careful examination of the equations by which Wald determines the values of the boundaries for tests of sequential hypotheses, interesting relationships for the conditional probability distributions of the stage at which the test terminates were obtained. These enable the study of sequential tests in which the boundaries are functions of the sample number. Particular concern was given to tests with convergent boundaries, and a set of boundaries which approach those of a truncated Wald test were investigated. Approximate expressions for the expected sample number and probabilities of error were obtained for the tests considered. The obtained approximations apply best for gently tapering slopes. Extensions of the method can be applied to evaluate various ad hoc schemes for truncating tests and to the theory of tests with a varying parameter.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1964
Accession Number
AD0452602

Entities

People

  • Julian J. Bussgang
  • Michael B. Marcus

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Energy and Power Technologies
  • Human Systems
  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Ballistic Missiles
  • Boundaries
  • Detectors
  • Equations
  • Errors
  • Hypotheses
  • Inequalities
  • Low Altitude
  • Observation
  • Phased Array Radar
  • Polynomials
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Random Walk
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Regression Analysis.