On Peters's formula for probable error

On the Näıve Error Formula for Bivariate Linear Interpolation

In this article we investigate a “näıve” error formula for linear bivariate interpolation. We show that such a formula exists if and only if the interpolation sites form the vertices of a right triangle with sides parallel to the axes. Hence the mere existence of a näıve error formula imposes a rather stringent limitation on the type of interpolation.

On Error Estimates for the Trotter-kato Product Formula

We study the error bound in the operator norm topology for the Trotter exponential product formula as well as for its generalization a la Kato. In the frame of the abstract setting we give a simple proof of error estimates which improve some of recent results in this direction.

An Error Estimate for Stenger's Quadrature Formula

The basis of this paper is the quadrature formula where q = exp(2A), h being a chosen step length. This formula has been derived from the Trapezoidal Rule formula by F. Stenger. An explicit form of the error is given for the case where the integrand has a factor of the form (1 — x)a(\ + x)P, a,ß> -1. Application is made to the evaluation of Cauchy principal value integrals with endpoint singula...

On Student’s 1908 Article “The Probable Error of a Mean”

This month marks the 100th anniversary of the appearance of William Sealey Gosset’s celebrated article, “The Probable Error of a Mean” (Student 1908a). Gosset’s elegant result represented the first in a series of exact, “small-sample” results that were developed by Gosset, Fisher, and others to form a central component of the modern theory of statistical inference. This review celebrates the ce...

The Probable Error of a Mean