On a property of the order statistics of the uniform distribution
Let be a sample from the uniform distribution on the interval (0, θ), where θ is unknown, and be the order statistics of the sample. Both statistics and are unbiased estimators of the population mean θ/2. Consider the change of the variances of Tk and Hk as k changes. We show that both D(Tk) and D(Hk) are strictly and Especially, When n is even, i.e.n = 2s, we obtian the following inequalities .