On the generalization of rao-cramer inequality

Let X₁, X₂, .., X_n denote a random sample of size n≥1 from a distribution with p.d.f. f(x; θ), θ ϵ Ω = (θ; α<θ<β), where α and β are known numbers. If Y = φ(X₁, X₂, …, X_n) is an unbiased estimator of parameter θ and σ²_y denote the variance of Y then according to the Rao-Cramer Inequality

In this paper, we shall present some generalizations and a refinement of this famous inequality.