title: The bounded inverse Weibull distribution: An extreme value alternative for application to environmental maxima?

authors: Bardsley, W. Earl

subjects: bounded extremes

abstract: There has long been interest in making inferences about future low-probability natural events that have magnitudes greater than any in the past record. Given a stationary time series, the unbounded Type 1 and Type 2 asymptotic extreme value distributions are often invoked as giving theoretical justification for extrapolating to large magnitudes and long return periods for hydrological variables such as rainfall and river discharge. However, there is a problem in that environmental extremes are bounded above by the bounded nature of their causal variables. Extrapolation using unbounded asymptotic models therefore cannot be justified from extreme value theory and at some point there will be over-prediction of future magnitudes. This creates the apparent contradiction, for example, of annual rainfall maxima being well approximated by Type 2 extreme value distributions despite the bounded nature of rainfall magnitudes. An alternative asymptotic extreme value approach is suggested for further investigation, with the model being the asymptotic distribution of minima (Weibull distribution) applied to block maxima reciprocals. Two examples are presented where data that are well matched by Type 1 or Type 2 extreme value distributions give reciprocals suggestive of lower bounds (upper bound γ to the original data). The asymptotic model here is a 3-parameter Weibull distribution for the reciprocals, with positive location parameter γ−1. When this situation is demonstrated from data, parameter estimation can be carried out with respect to the distribution of reciprocals of 3-parameter Weibull random variables. This distribution is referenced here as the bounded inverse Weibull distribution. A maximum likelihood parameter estimation methodology is presented, together with a parametric bootstrap approach for obtaining one-sided upper confidence limits to γ. When data permits estimation of γ, the bounded inverse Weibull distribution is suggested as an improved alternative to Type 1 or Type 2 extreme value distributions because the upper bound reality is recognised. However, extensive application to many data sets is required to evaluate the practical utility of the bounded approach for extrapolating beyond the largest recorded event.

text: The bounded inverse Weibull distribution: An extreme value alternative for application to environmental maxima? There has long been interest in making inferences about future low-probability natural events that have magnitudes greater than any in the past record. Given a stationary time series, the unbounded Type 1 and Type 2 asymptotic extreme value distributions are often invoked as giving theoretical justification for extrapolating to large magnitudes and long return periods for hydrological variables such as rainfall and river discharge. However, there is a problem in that environmental extremes are bounded above by the bounded nature of their causal variables. Extrapolation using unbounded asymptotic models therefore cannot be justified from extreme value theory and at some point there will be over-prediction of future magnitudes. This creates the apparent contradiction, for example, of annual rainfall maxima being well approximated by Type 2 extreme value distributions despite the bounded nature of rainfall magnitudes. An alternative asymptotic extreme value approach is suggested for further investigation, with the model being the asymptotic distribution of minima (Weibull distribution) applied to block maxima reciprocals. Two examples are presented where data that are well matched by Type 1 or Type 2 extreme value distributions give reciprocals suggestive of lower bounds (upper bound γ to the original data). The asymptotic model here is a 3-parameter Weibull distribution for the reciprocals, with positive location parameter γ−1. When this situation is demonstrated from data, parameter estimation can be carried out with respect to the distribution of reciprocals of 3-parameter Weibull random variables. This distribution is referenced here as the bounded inverse Weibull distribution. A maximum likelihood parameter estimation methodology is presented, together with a parametric bootstrap approach for obtaining one-sided upper confidence limits to γ. When data permits estimation of γ, the bounded inverse Weibull distribution is suggested as an improved alternative to Type 1 or Type 2 extreme value distributions because the upper bound reality is recognised. However, extensive application to many data sets is required to evaluate the practical utility of the bounded approach for extrapolating beyond the largest recorded event.

year: 2021

title: SEPSen: Semantic event processing at the sensor nodes for energy efficient wireless sensor networks

authors: Kasi, Mumraiz Khan

subjects: semanitcs

abstract: Traditionally in WSNs, the sensor nodes are used only for capturing data that is then later analyzed in the more powerful gateway nodes. This requires a continuous communication that wastes energy at the sensor nodes and greatly reduces the overall network lifetime. We propose a semantic-based in-network data processing that reduces energy consumption and improves the scalability of heterogeneous sensor networks. Ontology fragments in each sensor node help identify the data routed through the sensor network. We have adapted a matching algorithm to process a changing knowledge base. Simulation results show that the networks' energy consumption is considerably reduced.

text: SEPSen: Semantic event processing at the sensor nodes for energy efficient wireless sensor networks Traditionally in WSNs, the sensor nodes are used only for capturing data that is then later analyzed in the more powerful gateway nodes. This requires a continuous communication that wastes energy at the sensor nodes and greatly reduces the overall network lifetime. We propose a semantic-based in-network data processing that reduces energy consumption and improves the scalability of heterogeneous sensor networks. Ontology fragments in each sensor node help identify the data routed through the sensor network. We have adapted a matching algorithm to process a changing knowledge base. Simulation results show that the networks' energy consumption is considerably reduced.

year: 2012

title: Bones | Iwi

authors: Apiata, Hāwea

abstract: Poetry written at Kāwhia featured in Issue 6 of The Quick Brown Dog Journal published by Hagley Writers' Institute, Christchurch, NZ.

text: Bones | Iwi Poetry written at Kāwhia featured in Issue 6 of The Quick Brown Dog Journal published by Hagley Writers' Institute, Christchurch, NZ.

year: 2024-03-08