Volume 40 - Issue 2 - December 2015

In memoriam: François Jongmans (1921–2014), mathematical historian

Eugene Seneta

Abstract

After retirement from the University of Liège, François Jongmans wrote on the history of mathematics for 25 years. His initial focus on Eugène Charles Catalan (1814–1894) broadened to 19th century mathematics in Belgium and France, and extended to the history of geometric probability. A long-term interest was the gauging of wine barrels, a topic neglected for two centuries. The present personal tribute derives from a collaboration on some seven papers, and an intensive correspondence of over 20 years. It sets the work on geometric probability and particularly barrel-gauging in a self-contained context, with additional background from the correspondence. This tribute will be electronically accessible on Google under the above title after publication.

Some Catalan and Lobb delights

Thomas Koshy

Abstract

We investigate the combinatorially defined Lobb numbers with some new relationships to the ubiquitous Catalan numbers.

On sequences of independent Bernoulli trials avoiding the pattern '11 · · · 1'

Lingyun Zhang and Petros Hadjicostas

Abstract

For three types of 0–1 (Bernoulli) sequences of length n, where n >= 1, we show how to find the number of sequences that avoid the pattern '11 · · · 1' (d consecutive 1s, where d >= 2).

Most powerful goodness-of-fit test for prior density functions

Hamzeh Torabi and Saralees Nadarajah

Abstract

Some concepts for hypotheses testing about prior density functions based on a primary sample are given. We derive a Neyman–Pearson lemma to find a most powerful goodness-of-fit test for a prior distribution. A main benefit of the proposed test is that Bayesian statisticians may use the proposed test for choosing a suitable prior distribution and use that for ordinary Bayesian statistical inference. Finally, some examples are given.

Poisson and household size

V. E. Jennings and C. W. Lloyd-Smith

Abstract

In this paper we describe some recent work on the statistical modelling of household size distributions. This includes the use of age ratios using three major age groups (0–19, 20–59, and 60+), together with a Poisson distribution. We also provide a three-dimensional representation of the Poisson distribution which is linked with an associated gamma distribution. Connections are given in this work to a Poisson process model linked to births of children, and why it yields a successful statistical model.

From 'funny time, funny money' to realistic labour times

Xiaolin Luo, Pavel V. Shevchenko and Brad Sayer

Abstract

The motor vehicle retailing and services industry is one of the largest service industries in the developed world. A persistent issue concerning consumers, motor vehicle insurers, and smash repairers alike is how much a smash repairer should be paid for the paint labour time. While attempts are being made to replace the old system known in the smash repairs industry as 'funny time, funny money' by fairer systems based on empirical evidence, there is lack of rigorous analysis based on observed data and sound statistical methods. This paper proposes and calibrates a statistical model for estimating paint labour times, accounting for the inherently significant uncertainties in the paint process. Fine details such as flash-off time, the number of paint layers, and the number of coats per layer are included in the model. A series of experiments were conducted at various paint workshops over a few years to collect data for model calibration. It was found that, excluding drying time, paint labour times obey a simple relationship to the panel areas. A case study was performed to compare the model predicted upper bounds with an empirically developed commercial system of paint labour times.

Fibonacci walks

Thomas Koshy

Abstract

We introduce the family of Gibonacci polynomials. Using the concept of the weight of a Fibonacci walk, we present a combinatorial interpretation of Fibonacci polynomials and derive a few well-known Fibonacci polynomial identities. Finally, we establish a bijection between the set of Fibonacci walks of length n and the set of Fibonacci tilings of a 1 x n board.