Statistical Inference for Multiply Truncated Power Series Distributions

Abstract

Convolutions of one-parameter power series distributions (PSD) truncated on the left at several known or unknown points are studied via exponential generating functions. The special cases of the logarithmic series, the Poisson and the binomial and negative binomial distributions lead to multiparameter Stirling numbers of the first and second type and C-numbers respectively. Minimum variance unbiased estimators are found for certain functions of the parameters, including the probability functions themselves. Some conditional distribution properties are given and it is indicated how they can be used in confidence interval estimation of the reliability of multicomponent attribute failure models.

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Document Details

Document Type
Technical Report
Publication Date
Sep 30, 1974
Accession Number
ADA012990

Entities

People

  • T. Cacoullos

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Binomials
  • Computing-Related Activities
  • Convolution
  • Data Science
  • Estimators
  • Information Science
  • Interdisciplinary Science
  • Intervals
  • Mathematical Analysis
  • Mathematics
  • Power Series
  • Probability
  • Reliability
  • Statistical Analysis
  • Statistical Inference

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference