ON DISTRIBUTION’S CONSTANT SLOWLY VARYING COMPONENT

Abstract

In the present report it is proved that for a priori given numbers $\rho\in(1, +\infty)$ and $L\in R^+=(0, \infty)$ there is a distribution $\{p_n\}_1^\infty$ with the following properties: $\{p_n\}_1^\infty$ varies regularly as $n\rightarrow +\infty$ with exponent $(-\rho )$, exhibits the constant slowly varying component $L$, and $\{\log p_n\}_1^\infty$ is downward convex.