Abstract A properly scaled critical Galton–Watson process converges to a continuous state critical branching process <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>ξ</mi> <mo>⁢</mo> <mrow> <mo stretchy="false">(</mo> <mo lspace="4.2pt" rspace="4.2pt">⋅</mo> <mo stretchy="false">)</mo> </mrow> </mrow> </math><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>ξ</mi> <mo>⁢</mo> <mrow> <mo stretchy="false">(</mo> <mo lspace="4.2pt" rspace="4.2pt">⋅</mo> <mo stretchy="false">)</mo> </mrow> </mrow> </math> as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping generations and...

Abstract Di Crescenzo and Longobardi [Di Crescenzo and Longobardi, On cumulative entropies, J. Statist. Plann. Inference 139 2009, 12, 4072–4087] proposed the cumulative entropy (CE) as an alternative to the differential entropy. They presented an estimator of CE using empirical approach. In...

Abstract The traffic intensity (ρ) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server. Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and...