Variance of the MVUE for Lognormal Variance

Abstract

MVUE θ* of the parametric function θ = Σ _i–1 h _i , exp(b _i μ + c _i σ²) for a lognormal distribution LN(μ, σ²) is considered. The exact variance var(θ*) is given. Then the variance of the MVUE of the parametric function θ = var (Y) = exp(2μ) {exp(2σ²) – exp(σ²)} is explored: (i) for a random sample from the LN(μ, σ²) distribution, and (ii) for a lognormal regression.

KEY WORDS:

• Lognormal distribution
• Variance
• Minimum variance unbiased estimator
• Lognormal regression