On Estimators with Minimum Bias for a Binomial Distribution
S. Kh. Sirazhadinov · Theory of Probability and Its Applications · 1956
Let x be a random variable that conforms to a binomial distribution with parameters n , p. The paper deals with the determination of upper and lower estimators of x for arbitrary polynomals of the $n+1$-th degree. These estimators are the best uniformly on $[0,1]$. They are found for two different cases of determining the measure of deviation $\Delta $: \[ \begin{gathered} (a)\qquad \Delta = \mathop {\sup }\limits_{0 \leqq p \leqq 1} \left| {Mf_x - f(p)} \right|, \hfill \\ (b)\qquad \Delta = \mathop {\sup }\limits_{0 \leqq p \leqq 1} \left| {\frac{1}{p}Mf_x - f(p)} \right|. \hfill \\ \end{gathered} \] The results are given as formulas and are also presented as numerical tables.