Physical Sciences and Mathematics Commons^™

Combining Independent Tests Of Conditional Shifted Exponential Distribution, Abedel-Qader S. Al-Masri

Journal of Modern Applied Statistical Methods

The problem of combining n independent tests as n→∞ for testing that variables are uniformly distributed over the interval (0, 1) compared to their having a conditional shifted exponential distribution with probability density function f (xθ ) = e^{−(x−γθ)} , x ≥γθ , θ ∈[a,∞), a ≥ 0 was studied. This was examined for the case where θ₁, θ₂, … are distributed according to the distribution function (DF) F and when the DF is Gamma (1, 2). Six omnibus methods were compared via the Bahadur efficiency. It is shown that, as γ → 0 and …