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Aims to build on the work of Buckland and Hindle regarding statistical distribution as applied to the field of bibliometrics, particularly the use of empirical laws.

Gives examples of hyperbolic distributions that have a bearing on the bibliometric application, and discusses the characteristics of hyperbolic distributions and the Bradford distribution.

Hyperbolic distributions are the inevitable result of combinatorial necessity and a tendency to short‐term rational behaviour.

Supports Bradford's conclusion from his law, i.e. that to know about one's speciality, one must go outside it.

Recent studies indicating long term dependence in stock market indices have found a mean reversion process. However, studies using rescaled range (R/S) analysis have not found evidence of a mean reversion or ergodic process. Instead, evidence from these studies indicate either long term persistence in a nonperiodic cycle or short run Markovian dependence with no long term persistence. The purpose of this paper is to study the issue of long term dependence using rescaled range analysis. The empirical results obtained in this study support the persistent dependence/nonperiodic cycle results and suggest that the dependence arises from the general economic cycle.

It is well known that the laws of Leimkuhler, Mandelbrot, Lotka and the verbal formulation of Bradford's law are equivalent. In this note we prove an analogous framework of laws in which now the law of Zipf occurs instead of Mandelbrot's law. Laws in this group are Brookes' law and the graphical formulation of Bradford's law. We show that both groups of laws are very different in the sense that they are not even equal asymptotically for high rankings.

Since 1960, and especially during the past three years, many papers have appeared about particular manifestations and applications of a certain class of empirical laws to a field that may be labelled conveniently ‘Bibliometrics’. This term, resuscitated by Alan Pritchard (see page 348), denotes, in my paraphrase, quantitative treatment of the properties of recorded discourse and behaviour appertaining to it.

In this work, we estimated the different entropies like Shannon entropy, Rényi divergences, Csiszár divergence by using Jensen’s type functionals. The Zipf’s–Mandelbrot law and hybrid Zipf’s–Mandelbrot law are used to estimate the Shannon entropy. The Abel–Gontscharoff Green functions and Fink’s Identity are used to construct new inequalities and generalized them for m-convex function.

The purpose of this paper is to argue that a stationary-differenced autoregressive (AR) process with lag greater than 1, AR(q > 1), has certain properties that are consistent with a fractional Brownian motion (fBm). What the authors are interested in is the investigation of approaches to identifying the existence of persistent memory of one form or another for the purposes of simulating commodity (and other asset) prices. The authors show in theory, and with application to agricultural commodity prices the relationship between AR(q) and quasi-fBm.

In this paper the authors develop mathematical relationships in support of using AR(q > 1) processes for simulating quasi-fBm.

From theory the authors show that any AR(q) process is a stationary, self-similar process, with a lag structure that captures the essential elements of scaling and a fractional power law. The authors illustrate through various means the approach, and apply the quasi-fractional AR(q) process to agricultural commodity prices.

While the results can be applied to most time series of commodity prices, the authors limit the evaluation to the Gaussian case. Thus the approach does not apply to infinite-variance models.

The approach to using the structure of an AR(q > 1) model to simulate quasi-fBm is a simple approach that can be applied with ease using conventional Monte Carlo methods.

The authors believe that the approach to simulating quasi-fBm using standard AR(q > 1) models is original. The approach is intuitive and can be applied easily.