scholarly journals Effects of sample size on estimation of rainfall extremes at high temperatures

2016 ◽  
Author(s):  
Berry Boessenkool ◽  
Gerd Bürger ◽  
Maik Heistermann
Keyword(s):  
Sample Size ◽  
High Temperatures ◽  
Extreme Rainfall ◽  
Distribution Functions ◽  
Small Samples ◽  
Temperature Ranges ◽  
Ca 50 ◽  
High Precipitation ◽  
Limited Moisture ◽  
Precipitation Records

Abstract. High precipitation quantiles tend to rise with air temperature, following the so-called Clausius–Clapeyron scaling. This CC-scaling relation breaks down, or even reverts, for very high temperatures. In our study, we verify this reversal using a 60-year period of summer data in Germany. One of the suggested meteorological explanations is limited moisture supply, but our findings indicate that this behavior could also originate from simple undersampling. The number of observations in high temperature ranges is small, so extreme rainfall intensities following CC-scaling may not yet be recorded but logically possible. Because empirical quantile estimators using plotting positions drop with decreasing sample size, they cannot correct for this effect. By fitting distributions to the precipitation records and using their parametric quantile, we obtain estimates of rainfall intensities that continue to rise with temperature. This procedure requires far fewer values (ca. 50 for the 99.9 % quantile) to converge than classical order based empirical quantiles (ca. 700). From the evaluation of several distribution functions, the Wakeby distribution appears to capture the precipitation behavior better than the General Pareto Distribution (GPD). Despite being parametric, GPD estimators still show some underestimation in small samples.

scholarly journals Effects of sample size on estimation of rainfall extremes at high temperatures

2017 ◽  
Vol 17 (9) ◽  
pp. 1623-1629 ◽  
Author(s):  
Berry Boessenkool ◽  
Gerd Bürger ◽  
Maik Heistermann
Keyword(s):  
Sample Size ◽  
High Temperatures ◽  
Generalized Pareto Distribution ◽  
Small Sample ◽  
Small Samples ◽  
Climate Data ◽  
Rainfall Frequency ◽  
High Quantiles ◽  
Limited Moisture ◽  
Quantile Estimates

Abstract. High precipitation quantiles tend to rise with temperature, following the so-called Clausius–Clapeyron (CC) scaling. It is often reported that the CC-scaling relation breaks down and even reverts for very high temperatures. In our study, we investigate this reversal using observational climate data from 142 stations across Germany. One of the suggested meteorological explanations for the breakdown is limited moisture supply. Here we argue that, instead, it could simply originate from undersampling. As rainfall frequency generally decreases with higher temperatures, rainfall intensities as dictated by CC scaling are less likely to be recorded than for moderate temperatures. Empirical quantiles are conventionally estimated from order statistics via various forms of plotting position formulas. They have in common that their largest representable return period is given by the sample size. In small samples, high quantiles are underestimated accordingly. The small-sample effect is weaker, or disappears completely, when using parametric quantile estimates from a generalized Pareto distribution (GPD) fitted with L moments. For those, we obtain quantiles of rainfall intensities that continue to rise with temperature.

Growth in Self-Actualization (Personal Orientation Inventory) in Adult Encounter Groups

1981 ◽  
Vol 1 (1) ◽  
pp. 5-8
Author(s):  
Les Beach
Keyword(s):  
Sample Size ◽  
Personal Growth ◽  
Total Sample ◽  
Small Samples ◽  
Total Sample Size ◽  
Personal Orientation Inventory ◽  
Self Actualization ◽  
Personal Orientation

To test the efficacy of the Personal Orientation Inventory in assessing growth in self-actualization in relation to encounter groups and to provide a more powerful measure of such changes, pre- and posttest data from 3 highly comparable encounter groups (N = 43) were combined for analysis. Results indicated that the Personal Orientation Inventory is a sensitive instrument for assessing personal growth in encounter groups and that a larger total sample size provides more significant results than those reported for small samples (e. g., fewer than 15 participants).

Determination of Sample Size and Influencing Factors to Characterize Faulting in Jointed Concrete Pavements

2021 ◽  
pp. 036119812199670
Author(s):  
Ruohan Li ◽  
Jorge A. Prozzi
Keyword(s):  
Sample Size ◽  
Plain Concrete ◽  
Concrete Pavements ◽  
Portland Cement Concrete ◽  
Federal Highway ◽  
Significant Difference ◽  
Jointed Concrete Pavement ◽  
Functional Classes ◽  
High Precipitation ◽  
Departments Of Transportation

The objective of this study is to evaluate the field variability of jointed concrete pavement (JCP) faulting and its effects on pavement performance. The standard deviation of faulting along both the longitudinal and transverse directions are calculated. Based on these, the overall variability is determined, and the required sample sizes needed for a given precision at a certain confidence level are calculated and presented. This calculation is very important as state departments of transportation are required to report faulting every 0.1 mi to the Federal Highway Administration as required by the 2015 FAST Act. On average, twice the number of measurements are needed on jointed reinforced concrete pavements (JRCP) to achieve the same confidence and precision as on jointed plain concrete pavements (JPCP). For example, a sample size of 13 is needed to achieve a 95% confidence interval with a precision of 1.0 mm for average faulting of JPCP, while 26 measurements are required for JRCP ones. Average faulting was found to correlate with several climatic, structural, and traffic variables, while no significant difference was found between edge and outer wheelpath measurements. The application of Portland cement concrete overlay and the use of dowel bars (rather than aggregate interlock) are found to significantly reduce faulting. Older sections located on higher functional classes, and in regions of high precipitation or where the daily temperature change is larger, tend to have higher faulting, and might require larger samples sizes as compared with the rest when faulting surveys are to be conducted.

scholarly journals W.S. Gosset and Some Neglected Concepts in Experimental Statistics: Guinnessometrics II

2011 ◽  
Vol 6 (2) ◽  
pp. 252-277 ◽  
Author(s):  
Stephen T. Ziliak
Keyword(s):  
Experimental Design ◽  
Sample Size ◽  
Large Scale ◽  
Statistical Significance ◽  
Small Sample ◽  
Small Samples ◽  
Significant Advance ◽  
Economic Approach ◽  
Barley Malt ◽  
Level Of Significance

AbstractStudent's exacting theory of errors, both random and real, marked a significant advance over ambiguous reports of plant life and fermentation asserted by chemists from Priestley and Lavoisier down to Pasteur and Johannsen, working at the Carlsberg Laboratory. One reason seems to be that William Sealy Gosset (1876–1937) aka “Student” – he of Student'st-table and test of statistical significance – rejected artificial rules about sample size, experimental design, and the level of significance, and took instead an economic approach to the logic of decisions made under uncertainty. In his job as Apprentice Brewer, Head Experimental Brewer, and finally Head Brewer of Guinness, Student produced small samples of experimental barley, malt, and hops, seeking guidance for industrial quality control and maximum expected profit at the large scale brewery. In the process Student invented or inspired half of modern statistics. This article draws on original archival evidence, shedding light on several core yet neglected aspects of Student's methods, that is, Guinnessometrics, not discussed by Ronald A. Fisher (1890–1962). The focus is on Student's small sample, economic approach to real error minimization, particularly in field and laboratory experiments he conducted on barley and malt, 1904 to 1937. Balanced designs of experiments, he found, are more efficient than random and have higher power to detect large and real treatment differences in a series of repeated and independent experiments. Student's world-class achievement poses a challenge to every science. Should statistical methods – such as the choice of sample size, experimental design, and level of significance – follow the purpose of the experiment, rather than the other way around? (JEL classification codes: C10, C90, C93, L66)

SMALL SAMPLE SIZE SCIENTIST

PEDIATRICS ◽  
1989 ◽  
Vol 83 (3) ◽  
pp. A72-A72
Author(s):  
Student
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Causal Explanation ◽  
Small Sample Size ◽  
Small Sample ◽  
Small Samples ◽  
High Expectations ◽  
Sampling Variation ◽  
The Law ◽  
The Stability

The believer in the law of small numbers practices science as follows: 1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power. 2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance. 3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals. 4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.

scholarly journals The use of personal weather station observations to improve precipitation estimation and interpolation

2021 ◽  
Vol 25 (2) ◽  
pp. 583-601
Author(s):  
András Bárdossy ◽  
Jochen Seidel ◽  
Abbas El Hachem
Keyword(s):  
Spatial Interpolation ◽  
Empirical Distribution ◽  
Precipitation Amount ◽  
Distribution Functions ◽  
Quantile Mapping ◽  
Novel Approach ◽  
Precipitation Estimation ◽  
Weather Stations ◽  
High Precipitation ◽  
Empirical Distribution Functions

Abstract. The number of personal weather stations (PWSs) with data available through the internet is increasing gradually in many parts of the world. The purpose of this study is to investigate the applicability of these data for the spatial interpolation of precipitation using a novel approach based on indicator correlations and rank statistics. Due to unknown errors and biases of the observations, rainfall amounts from the PWS network are not considered directly. Instead, it is assumed that the temporal order of the ranking of these data is correct. The crucial step is to find the stations which fulfil this condition. This is done in two steps – first, by selecting the locations using the time series of indicators of high precipitation amounts. Then, the remaining stations are then checked for whether they fit into the spatial pattern of the other stations. Thus, it is assumed that the quantiles of the empirical distribution functions are accurate. These quantiles are then transformed to precipitation amounts by a quantile mapping using the distribution functions which were interpolated from the information from the German National Weather Service (Deutscher Wetterdienst – DWD) data only. The suggested procedure was tested for the state of Baden-Württemberg in Germany. A detailed cross validation of the interpolation was carried out for aggregated precipitation amount of 1, 3, 6, 12 and 24 h. For each of these temporal aggregations, nearly 200 intense events were evaluated, and the improvement of the interpolation was quantified. The results show that the filtering of observations from PWSs is necessary as the interpolation error after the filtering and data transformation decreases significantly. The biggest improvement is achieved for the shortest temporal aggregations.

scholarly journals Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization

2019 ◽  
Vol 33 ◽  
pp. 2304-2313 ◽  
Author(s):  
Ken Kobayashi ◽  
Naoki Hamada ◽  
Akiyoshi Sannai ◽  
Akinori Tanaka ◽  
Kenichi Bannai ◽  
...  
Keyword(s):  
Sample Size ◽  
Optimization Problems ◽  
Solution Set ◽  
Small Samples ◽  
High Dimensional ◽  
Large Sample Size ◽  
Multi Objective Optimization ◽  
Dimensional Solution ◽  
Multi Objective ◽  
Simplex Model

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M − 1)-dimensional topological simplex (a curved line for M = 2, a curved triangle for M = 3, a curved tetrahedron for M = 4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bézier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bézier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the postoptimization process and enable a better trade-off analysis.

Using Data From Personal Weather Stations to Improive Precipitation Estimation and Interpolation

2020 ◽  
Author(s):  
Jochen Seidel ◽  
Abbas El Hachem ◽  
András Bárdossy
Keyword(s):  
Spatial Interpolation ◽  
Cross Validation ◽  
Temporal Order ◽  
Distribution Functions ◽  
Secondary Network ◽  
Precipitation Estimation ◽  
Weather Stations ◽  
High Precipitation ◽  
Using Data ◽  
Service Data

<p>The number of private meteorological stations with data available online through the internet is increasing gradually in many parts of the world. The purpose of this study is to investigate the applicability of these data for the spatial interpolation of precipitation for high intensity events of different durations. Due to unknown biases of the observations, rainfall amounts of the secondary network are not considered directly. Instead, only their temporal order is assumed to be correct. The crucial step is to find the stations with informative measurements. This is done in two steps, first by selecting the locations using time series of indicators of high precipitation amounts. The remaining stations are checked whether they fit into the spatial pattern of the other stations. Thus it is assumed that the percentiles at the secondary network accurate. These percentiles are then translated to precipitation amounts using the distribution functions which were interpolated using the weather service data only. The suggested procedure was tested for the State of Baden-Württemberg in Germany. A detailed cross validation of the interpolation was carried out for aggregated precipitation amounts of 1, 3, 6, 12 and 24 hours. For each aggregations, nearly 200 intense events were evaluated. The results show that filtering the secondary observations is necessary, the interpolation error after filtering and data transformation decreases significantly. The biggest improvement is achieved for the shortest time aggregations.</p>

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