On some analogs of Rao-Cramér inequality and a series of inequalities satisfied by the gamma function (Q1063350)

The present paper is mostly expository in nature. It may be divided into two parts. The first part describes Rao-Cramér inequality of statistical estimation theory and collects several of its analogues, improvements and generalizations, which are scattered over a number of statistical and other journals. The second half of the paper describes Gurland's inequality satisfied by the gamma function which was derived by applying the Rao-Cramér inequality and collects several of its analogues, improvements and generalizations obtained by applying the corresponding extensions.