title: The Weibull distribution as an extreme value model for transformed annual maxima

authors: Bardsley, W. Earl

subjects: Weibull distribution

abstract: There is no mathematical difference between theoretical extreme value models of maxima and minima because they link to each other by a simple sign reversal transformation. However, other transformations that change sample maxima to sample minima raise the possibility of alternatives to the generalised extreme value (GEV) distribution for annual maxima, while still maintaining extreme value justification. A general class of transformation is proposed that converts positive annual maxima to lower-bounded minima, then amenable to Weibull extreme value analysis for sufficiently large sample sizes. That is, the Weibull distribution of smallest extremes provides a theoretical extreme value model for the transformed maxima, which holds irrespective of any GEV form of the original maxima. This would apply, for example, to the analysis of reciprocals of discharge or rainfall annual maxima.
A useful feature of the transformation approach is that alternative prediction expressions with extreme value justification can arise for defining event magnitude as a function of return period. These expressions may result in different hydrological conclusions than from a GEV analysis of maxima. A double exponential transformation is introduced and its prediction function for maxima is noted to have capability to mimic equivalent Type 3 extreme value (EV3) distribution expressions, but without having to introduce an upper bound parameter. The new function gives a good fit to apparent EV3 annual flood maxima recorded from two very different catchments: the Yangtze River in China and the upper Whanganui River in New Zealand.

text: The Weibull distribution as an extreme value model for transformed annual maxima There is no mathematical difference between theoretical extreme value models of maxima and minima because they link to each other by a simple sign reversal transformation. However, other transformations that change sample maxima to sample minima raise the possibility of alternatives to the generalised extreme value (GEV) distribution for annual maxima, while still maintaining extreme value justification. A general class of transformation is proposed that converts positive annual maxima to lower-bounded minima, then amenable to Weibull extreme value analysis for sufficiently large sample sizes. That is, the Weibull distribution of smallest extremes provides a theoretical extreme value model for the transformed maxima, which holds irrespective of any GEV form of the original maxima. This would apply, for example, to the analysis of reciprocals of discharge or rainfall annual maxima.
A useful feature of the transformation approach is that alternative prediction expressions with extreme value justification can arise for defining event magnitude as a function of return period. These expressions may result in different hydrological conclusions than from a GEV analysis of maxima. A double exponential transformation is introduced and its prediction function for maxima is noted to have capability to mimic equivalent Type 3 extreme value (EV3) distribution expressions, but without having to introduce an upper bound parameter. The new function gives a good fit to apparent EV3 annual flood maxima recorded from two very different catchments: the Yangtze River in China and the upper Whanganui River in New Zealand.

year: 2019

title: Modeling seasonality in new product diffusion

authors: Peers, Y.

subjects: diffusion models

abstract: We propose a method to include seasonality in any diffusion model that has a closed-form solution. The resulting diffusion model captures seasonality in a way that naturally matches the original diffusion model’s pattern. The method assumes that additional sales at seasonal peaks are drawn from previous or future periods. This implies that the seasonal pattern does not inﬂuence the underlying diffusion pattern. The model is compared with alternative approaches through simulations and empirical examples. As alternatives, we consider the standard Generalized Bass Model (GBM) and the basic Bass Model, which ignores seasonality. One of the main ﬁndings is that modeling seasonality in a GBM generates good predictions but gives biased estimates. In particular, the market potential parameter is underestimated. Ignoring seasonality in cases where data of the entire diffusion period are available gives unbiased parameter estimates in most relevant scenarios. However,ignoring seasonality leads to biased parameter estimates and predictions when only part of the diffusion period is available. We demonstrate that our model gives correct estimates and predictions even if the full diffusion process is not yet available.

text: Modeling seasonality in new product diffusion We propose a method to include seasonality in any diffusion model that has a closed-form solution. The resulting diffusion model captures seasonality in a way that naturally matches the original diffusion model’s pattern. The method assumes that additional sales at seasonal peaks are drawn from previous or future periods. This implies that the seasonal pattern does not inﬂuence the underlying diffusion pattern. The model is compared with alternative approaches through simulations and empirical examples. As alternatives, we consider the standard Generalized Bass Model (GBM) and the basic Bass Model, which ignores seasonality. One of the main ﬁndings is that modeling seasonality in a GBM generates good predictions but gives biased estimates. In particular, the market potential parameter is underestimated. Ignoring seasonality in cases where data of the entire diffusion period are available gives unbiased parameter estimates in most relevant scenarios. However,ignoring seasonality leads to biased parameter estimates and predictions when only part of the diffusion period is available. We demonstrate that our model gives correct estimates and predictions even if the full diffusion process is not yet available.

year: 2012

title: Participatory data design: managing data sovereignty in IoT solutions

authors: Bowen, Judy

subjects: computer science

abstract: Within the software engineering community, deciding how to collect, store and use personal data has become about more than just understanding our users. This paper considers ethical data use which includes cultural considerations and data ownership rights. We discuss indigenous data sovereignty as a concept and how it potentially impacts technological solutions that gather personal data from users. We propose an extension to typical user-centred design processes which we call participatory data design. This incorporates the use of frameworks and tools that specifically focus on managing data within the cultural context it is gathered from. We also present a specific example of how we have used this approach in the context of a data collection project from M¯aori workers in New Zealand forestry. We conclude with a discussion of the wider implications of this approach.

text: Participatory data design: managing data sovereignty in IoT solutions Within the software engineering community, deciding how to collect, store and use personal data has become about more than just understanding our users. This paper considers ethical data use which includes cultural considerations and data ownership rights. We discuss indigenous data sovereignty as a concept and how it potentially impacts technological solutions that gather personal data from users. We propose an extension to typical user-centred design processes which we call participatory data design. This incorporates the use of frameworks and tools that specifically focus on managing data within the cultural context it is gathered from. We also present a specific example of how we have used this approach in the context of a data collection project from M¯aori workers in New Zealand forestry. We conclude with a discussion of the wider implications of this approach.

year: 2022