Estimation of Starshaped Sequences of Poisson and Normal Means

A vector μ = (μ₁, ⋯, μₙ) is said to be upper [lower] starshaped if μm + 1 0 μm + 1 μ̄ₘ m = 1, ⋯, n - 1, where μ̄ₘ is a weighted average of μ₁, ⋯, μₘ. Obtained is the maximum likelihood estimate of μ when the μᵢ's are the means of n Poisson or normal populations and μ is known to be starshaped. The method is applied to obtain estimators of IHRA (increasing hazard rate average) distribution functions.