In 2005, Yatracos constructed the estimator <italic>S</italic> -super-2 ₂ = <italic>c</italic> ₂ <italic>S</italic> -super-2, <italic>c</italic> ₂ = (<italic>n</italic> + 2)(<italic>n</italic> − 1)[<italic>n</italic>(<italic>n</italic> + 1)]-super-− 1, of the variance, which has smaller mean squared error (MSE) than the unbiased estimator <italic>S</italic> -super-2. In this work, the estimator <italic>S</italic> -super-2 ₁ = <italic>c</italic> ₁ <italic>S</italic> -super-2, <italic>c</italic> ₁ = <italic>n</italic>(<italic>n</italic> −...

A monotone likelihood ratio property is shown to hold for the inverse Gaussian distribution. Applications of this property in decision theoretic point and interval estimation of the lambda parameter are indicated.

In a recent paper Basu and Ghosh (1980) established weak consistency and asymptotic normality of a solution to the likelihood equation in two important cases arising in life testing under type I censoring. In this paper we supplement the work of Basu and Ghosh by establishing strong consistency....