Hypothesis Testing and Confidence Intervals for Products and Quotients of Poisson Parameters with Applications to Reliability

Abstract

X₁ X₂, ···, X_k1, Y₁, Y₂, ···, Y_k2 are k₁ + k₂ mutually independent Poisson random variables with parameters λ₁, λ₂, ···, λ_k1, μ₁, μ₂, ···, μ_k2, respectively. Confidence intervals and tests of hypotheses for the parameter θ = λ₁λ₂ ··· λ_k1 / μ₁μ₂ ··· μ_k2 are obtained. Under suitable conditions these procedures may be used to obtain approximate confidence intervals and tests of hypotheses of the parameter ρ = ρ₁ρ₂ ··· ρ_k1/ρ_k1+1ρ_k1+² ··· ρ_k1+k₂, where the ρi's, i = 1, 2, ···, k₁ + k₂ are binomial parameters. This problem is of importance in reliability analysis and some applications to reliability analysis are exhibited.