Order Statistics and Clinical-Practice Studies

2018 ◽  
Vol 3 (2) ◽  
pp. 13-30
Author(s):  
E Jack Chen
Keyword(s):  
Order Statistics ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Quantile Estimation ◽  
Cumulative Distribution ◽  
Test Interpretation ◽  
Hypothesis Tests ◽  
Parametric Statistics ◽  
Goodness Of Fit Hypothesis ◽  
Tests Of Independence

Statistics are essential tools in scientific studies and facilitate various hypothesis tests, such as test administration, response scoring, data analysis, and test interpretation. Order statistics refer to the collection of sample observations sorted in ascending order and are among the most fundamental tools in non-parametric statistics and inference. Statistical inference established based on order statistics assumes nothing stronger than continuity of the cumulative distribution function of the population and is simple and broadly applicable. The authors discuss how order statistics are applied in statistical analysis, e.g., tests of independence, tests of goodness of fit, hypothesis tests of equivalence of means, ranking and selection, and quantile estimation. These order-statistics techniques are key components of many clinical studies.

Order Statistics and Applications

2018 ◽  
pp. 1856-1868
Author(s):  
E. Jack Chen
Keyword(s):  
Distribution Function ◽  
Statistical Analysis ◽  
Order Statistics ◽  
Goodness Of Fit ◽  
Ranking And Selection ◽  
Quantile Estimation ◽  
Cumulative Distribution ◽  
Parametric Statistics ◽  
Goodness Of Fit Hypothesis ◽  
Tests Of Independence

Order statistics refer to the collection of sample observations sorted in ascending order and are among the most fundamental tools in non-parametric statistics and inference. Statistical inference established based on order statistics assumes nothing stronger than continuity of the cumulative distribution function of the population and is simple and broadly applicable. We discuss how order statistics are applied in statistical analysis, e.g., tests of independence, tests of goodness of fit, hypothesis tests of equivalence of means, ranking and selection, and quantile estimation. These order-statistics techniques are key components of many studies.

Order Statistics and Applications

2019 ◽  
pp. 440-457
Author(s):  
E. Jack Chen
Keyword(s):  
Distribution Function ◽  
Statistical Analysis ◽  
Order Statistics ◽  
Goodness Of Fit ◽  
Ranking And Selection ◽  
Quantile Estimation ◽  
Cumulative Distribution ◽  
Parametric Statistics ◽  
Goodness Of Fit Hypothesis ◽  
Tests Of Independence

Order statistics refer to the collection of sample observations sorted in ascending order and are among the most fundamental tools in non-parametric statistics and inference. Statistical inference established based on order statistics assumes nothing stronger than continuity of the cumulative distribution function of the population and is simple and broadly applicable. The authors discuss how order statistics are applied in statistical analysis (e.g., tests of independence, tests of goodness of fit, hypothesis tests of equivalence of means, ranking and selection, and quantile estimation). These order-statistics techniques are key components of many studies.

Order Statistics in Simulation

2014 ◽  
pp. 1750-1761 ◽  
Author(s):  
E Jack Chen
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Order Statistics ◽  
Statistical Inference ◽  
Goodness Of Fit ◽  
Ranking And Selection ◽  
Cumulative Distribution ◽  
Parametric Statistics ◽  
Goodness Of Fit Hypothesis ◽  
Tests Of Independence

Order statistics refer to the collection of sample observations sorted in ascending order and are among the most fundamental tools in non-parametric statistics and inference. Statistical inference established based on order statistics assumes nothing stronger than continuity of the cumulative distribution function of the population and is simple and broadly applicable. We discuss how order statistics are applied in computer simulation, e.g., tests of independence, tests of goodness of fit, hypothesis tests of equivalence of means, ranking and selection, and quantiles estimation. These order-statistics techniques are key components of many simulation studies.

scholarly journals On the Consistency of the Two-Sample Empty Cell Test

1964 ◽  
Vol 7 (1) ◽  
pp. 57-63 ◽  
Author(s):  
M. Csorgo ◽  
Irwin Guttman
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Empty Cell ◽  
Independent Observations ◽  
Cell Test

This paper considers the consistency of the two-sample empty cell test suggested by S. S. Wilks [2]. A description of this test is as follows: Let a sample of n1 independent observations be taken from a population whose cumulative distribution function F1(x) is continuous, but 1 otherwise unknown. Let X(1) < X(2) < … < X(n1) be their order statistics. Let a second sample of n2 observations be taken from a population whose cumulative distribution function is F2(x), assumed continuous, but otherwise unknown.

scholarly journals Results of the Verification of the Statistical Distribution Model of Microseismicity Emission Characteristics

2016 ◽  
Vol 61 (3) ◽  
pp. 489-496
Author(s):  
Aleksander Cianciara
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Statistical Distribution ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Emission Characteristics ◽  
Goodness Of Fit Test ◽  
Empirical Cumulative Distribution Function

Abstract The paper presents the results of research aimed at verifying the hypothesis that the Weibull distribution is an appropriate statistical distribution model of microseismicity emission characteristics, namely: energy of phenomena and inter-event time. It is understood that the emission under consideration is induced by the natural rock mass fracturing. Because the recorded emission contain noise, therefore, it is subjected to an appropriate filtering. The study has been conducted using the method of statistical verification of null hypothesis that the Weibull distribution fits the empirical cumulative distribution function. As the model describing the cumulative distribution function is given in an analytical form, its verification may be performed using the Kolmogorov-Smirnov goodness-of-fit test. Interpretations by means of probabilistic methods require specifying the correct model describing the statistical distribution of data. Because in these methods measurement data are not used directly, but their statistical distributions, e.g., in the method based on the hazard analysis, or in that that uses maximum value statistics.

scholarly journals Exact distributions of order statistics from ln,p-symmetric sample distributions

2017 ◽  
Vol 5 (1) ◽  
pp. 221-245 ◽  
Author(s):  
K. Müller ◽  
W.-D. Richter
Keyword(s):  
Distribution Function ◽  
Finite Number ◽  
Order Statistics ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Symmetric Distributions ◽  
Sample Distribution ◽  
Special Cases ◽  
Exact Distributions ◽  
Gaussian Sample

Abstract We derive the exact distributions of order statistics from a finite number of, in general, dependent random variables following a joint ln,p-symmetric distribution. To this end,we first review the special cases of order statistics fromspherical aswell as from p-generalized Gaussian sample distributions from the literature. To study the case of general ln,p-dependence, we use both single-out and cone decompositions of the events in the sample space that correspond to the cumulative distribution function of the kth order statistic if they are measured by the ln,p-symmetric probability measure.We show that in each case distributions of the order statistics from ln,p-symmetric sample distribution can be represented as mixtures of skewed ln−ν,p-symmetric distributions, ν ∈ {1, . . . , n − 1}.

scholarly journals An objective cross-validation framework for mapping rainfall hazard based on rain gauge data

2018 ◽  
Author(s):  
Juliette Blanchet ◽  
Emmanuel Paquet ◽  
Pradeebane Vaittinada Ayar ◽  
David Penot
Keyword(s):  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Cross Validation ◽  
Daily Rainfall ◽  
Rain Gauge ◽  
Cumulative Distribution ◽  
Rain Gauge Data ◽  
Weather Patterns ◽  
Rain Gauges ◽  
Validation Framework

Abstract. We propose an objective framework for estimating rainfall cumulative distribution function within a region when data are only available at rain gauges. Our methodology is based on the evaluation of several goodness-of-fit scores in a cross-validation framework, allowing to assess goodness-of-fit of the full distribution but with a particular focus on its tail. Cross-validation is applied both to select the most appropriate statistical distribution at station locations and to validate the mapping of these distributions. Our methodology is applied to daily rainfall in the Ardèche catchment in South of France, a 2260 km2 catchment with strong disparities in rainfall distribution. Results show preference for a mixture of Gamma distribution over seasons and weather patterns, with parameters interpolated with thin plate spline across this region. However the framework presented in this paper is general and could be likewise applied in any region, with possibly different conclusion depending on the subsequent rainfall processes.

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