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Related Concept Videos

Outliers and Influential Points01:08

Outliers and Influential Points

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An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the...
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What Are Outliers?01:12

What Are Outliers?

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Outliers are observed data points that are far from the least squares line. They have unusual values and need to be examined carefully. Though an outlier may result from erroneous data, at other times, it may hold valuable information about the population under study and should be included in the data. Hence, it is crucial to examine what causes a data point to be an outlier.
The z score is used to find outliers or unusual values. It should be noted that any values beyond -2 and +2 are...
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Cluster Sampling Method01:20

Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
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Microsoft Excel: Finding Central Tendency, Skew, and Kurtosis01:24

Microsoft Excel: Finding Central Tendency, Skew, and Kurtosis

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Central tendency refers to the central point or typical value of a dataset. It summarizes the data set with a single value that represents the center of its distribution. The three main measures of central tendency are:
Mean: The arithmetic average of all data points. It is calculated by adding all the values together and dividing by the number of values. The mean is sensitive to extreme values (outliers).
Median: The middle value when the data points are arranged in ascending or descending...
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Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

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Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...
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Unusual Results01:16

Unusual Results

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Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value =...
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ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
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Clustering of extreme values: estimation and application.

Marta Ferreira1

  • 1Centro de Matemática, Universidade do Minho, Braga, Portugal.

Advances in Statistical Analysis : Asta : a Journal of the German Statistical Society
|June 26, 2023
PubMed
Summary

Extreme value theory (EVT) helps assess risks from extreme events. This study refines the extremal index, a key EVT measure for extreme value clustering, by comparing automatic estimation methods.

Area of Science:

  • Extreme value theory (EVT)
  • Statistical modeling
  • Risk assessment

Background:

  • Extreme value theory (EVT) provides methods for risk inference across diverse fields like finance, climate science, and engineering.
  • The clustering of extreme values significantly impacts the risk of extreme phenomena, seen in droughts, floods, and market crashes.
  • The extremal index quantifies extreme value clustering, crucial for understanding and managing associated risks.

Purpose of the Study:

  • To revisit and compare existing extremal index estimators.
  • To apply and evaluate automatic threshold and clustering parameter selection methods.
  • To assess the performance of different extremal index estimation techniques.

Main Methods:

  • Review of established extremal index estimation methodologies.

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  • Implementation of automated methods for threshold selection.
  • Application of automated techniques for clustering parameter identification.
  • Comparative analysis of estimator performance.

    • Main Results:

    • Identification of optimal automatic methods for threshold and clustering parameter selection.
    • Performance comparison of various extremal index estimators under different conditions.
    • Demonstration of practical application using meteorological data.

    Conclusions:

    • Automated methods enhance the reliability of extremal index estimation.
    • The study provides a comparative framework for selecting appropriate EVT methods.
    • Findings are applicable to real-world risk assessment in fields like meteorology.