title: A simplified levelling instrument: the A-frame

authors: Riley, S.J.

abstract: A levelling instrument has been developed which permits work in a high degree of detail without field assistance.

text: A simplified levelling instrument: the A-frame A levelling instrument has been developed which permits work in a high degree of detail without field assistance.

year: 1969

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: Report on the bicultural symposium at conference

authors: Masters-Awatere, Bridgette

subjects: Maori

abstract: Kia ora koutou. I decided to submit the current paper as a way to say thank you to the large group of people in attendance at the bicultural stream at the national conference in late August that was held at Waikato University. It was their continued presence and participation that served as a catalyst and motivator for this paper. I'm conscious that while there was a large number of people in the symposium, there were other streams occurring at the same time, so I thought giving an overview of the success of the symposium would be a good way to let people know who the symposium went. However, before talking specifically about the symposium, I'd like to give mention to other events of the day...

text: Report on the bicultural symposium at conference Kia ora koutou. I decided to submit the current paper as a way to say thank you to the large group of people in attendance at the bicultural stream at the national conference in late August that was held at Waikato University. It was their continued presence and participation that served as a catalyst and motivator for this paper. I'm conscious that while there was a large number of people in the symposium, there were other streams occurring at the same time, so I thought giving an overview of the success of the symposium would be a good way to let people know who the symposium went. However, before talking specifically about the symposium, I'd like to give mention to other events of the day...

year: 2007