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# Trends in environmental data: when uncertainty matters

Jaarsma, K.C.R. (2013) Trends in environmental data: when uncertainty matters. Master's Thesis / Essay, Mathematics.

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## Abstract

A lot of research is done on the behavior of environmental processes. Questions like how did these processes behave in the past and how will it behave in the future, are of interest. Within this context trend analysis is an important tool in the study of observed environmental data. Trend values are estimators of the observations or predictions of the future observations. Both the degree of uncertainty of this values and the detection of significant increase or decrease of the trend is of great importance. It is, because it contributes to a better prediction or estimation. There is extensive literature on trend estimation. Also several papers exist about uncertainty in trend estimation in the form of a point wise confidence interval for the trend estimates. About uncertainty in trend differences is also written in some articles. But full uncertainty information is missing for statistics such as return periods or the chance of crossing thresholds. My thesis will give renewal in the sense that it will describe a way to find this uncertainty information. I will present a way to find two new confidence intervals. The first one is a simultaneous confidence band for the generated trend and trend differences. The second confidence interval (as well point wise as simultaneous) is that of the exceedance of any threshold level. Besides giving a procedure to produce this, a new program in R will be presented called TrendspotteR 1.0. In TrendspotteR 1.0 a trend, trend differences, exceedance and differences in this exceedance of a threshold will be generated with maximum information on uncertainty. In the last chapter I will discuss a relevant expansion of TrendSpotteR 1.0 to estimate trends in data sets which contain some huge outliers and are distributed according to the Gumbel distribution.

Item Type: Thesis (Master's Thesis / Essay) Mathematics Master's Thesis / Essay English 15 Feb 2018 07:52 15 Feb 2018 07:52 http://fse.studenttheses.ub.rug.nl/id/eprint/10901

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