We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates ...

Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions. They used Laplace's method for asymptotic evaluation of integrals, in which ...

Exponential graphs are graphs in the form \(y = k^x\). These graphs increase rapidly in the \(y\) direction and will never fall below the \(x\)-axis.

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...

Exponential graphs are graphs in the form \(y = k^x\). These graphs increase rapidly in the \(y\) direction and will never fall below the \(x\)-axis.