Despite hazard and reversed hazard rates sharing a number of similar aspects, reversed hazard functions are far less frequently used. Understanding their meaning is not a simple task. The aim of this paper is to expand the usefulness of the reversed hazard function by relating it to other well-known concepts broadly used in economics: (linear or cumulative) rates of increase and elasticity. This will make it possible (i) to improve our understanding of the consequences of using a particular distribution and, in certain cases, (ii) to introduce our hypotheses and knowledge about the random process in a more meaningful and intuitive way, thus providing a means to achieving distributions that would otherwise be hardly imaginable or justifiable.

No abstract

No abstract

There is a growing tendency in credit card industry to increase the contribution of the smallest players, the cardholders, in the detection of card incidents. This article examines whether cardholders are efficient at detecting/communicating incidents of theft, loss or fraudulent use of their cards. The analysis focuses on whether they demonstrate enough speed of response to support a risk control subsystem by the issuer. The research follows a completely new approach showing how the issue can be handled by applying the concept of elasticity, a notion just recently exported from economics to the field of statistics by linking it with the reverse hazard rate. The issue is focused on the analysis of the characteristics of the elasticity function of the random variable that measures the delay of cardholders in reporting incidents. This study is illustrated with an application to a real data set of 1069 incidents.

The correct identification of change‐points during ongoing outbreak investigations of infectious diseases is a matter of paramount importance in epidemiology, with major implications for the management of health care resources, public health and, as the COVID‐19 pandemic has shown, social live. Onsets, peaks, and inflexion points are some of them. An onset is the moment when the epidemic starts. A "peak" indicates a moment at which the incorporated values, both before and after, are lower: a maximum. The inflexion points identify moments in which the rate of growth of the incorporation of new cases changes intensity. In this study, after interpreting the concept of elasticity of a random variable in an innovative way, we propose using it as a new simpler tool for anticipating epidemic remission change‐points. In particular, we propose that the "remission point of change" will occur just at the instant when the speed in the accumulation of new cases is lower than the average speed of accumulation of cases up to that moment. This gives stability and robustness to the estimation in the event of possible remission variations. This descriptive measure, which is very easy to calculate and interpret, is revealed as informative and adequate, has the advantage of being distribution‐free and can be estimated in real time, while the data is being collected. We use the 2014‐2016 Western Africa Ebola virus epidemic to demonstrate this new approach. A couple of examples analyzing COVID‐19 data are also included.