Binomial Distribution: Hypothesis Testing, Confidence Intervals (CI), and Reliability with Implementation in S-PLUS

Abstract

System requirements can be expressed in terms of an upper (lower) limit on the probability of failure (success). Statistical analysis of such binary (0/1, success/failure, go/no-go) data typically requires point and interval estimation and inference or hypothesis tests on the associated event probability. For identical independent trials, the proportion observed serves as an estimate of the event rate. Based on the method of Clopper-Pearson (CP) and the likelihood ratio (LR) technique properties of the binomial distribution are used to derive interval estimates, which are in turn used in inference. An application is the determination of sample size and maximum permissible number of failures (nf) required to establish a specific reliability (probability of success) with given probability (confidence).

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2010
Accession Number
ADA523927

Entities

People

  • Joseph C. Collins

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Binomials
  • Confidence Limits
  • Data Science
  • Discrete Distribution
  • Distribution Functions
  • Equations
  • Information Science
  • Intervals
  • Military Research
  • Probability
  • Probability Density Functions
  • Random Variables
  • Reliability
  • Standards
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference