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Related Concept Videos

Probability Distributions01:32

Probability Distributions

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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
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F Distribution01:19

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The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of freedom; one for the numerator and one for the denominator. The F distribution is derived from the Student's t distribution. The values of the F distribution are squares of the corresponding values of the t distribution. One-Way ANOVA expands the t test for comparing more than two groups. The scope of that derivation is beyond the level of this...
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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Reliability of pair distribution function analysis in in situ experiments.

Rasmus Baden Stubkjær1, Magnus Kløve1, Andreas Bertelsen1

  • 1Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO) Aarhus University Langelandsgade 140 Aarhus8000-DK Denmark.

Journal of Applied Crystallography
|April 2, 2025
PubMed
Summary

Quantifying experimental uncertainty in in situ pair distribution function (PDF) studies is crucial. Consistent parameter selection and processing algorithms ensure reliable results for nanoparticle synthesis and material science research.

Keywords:
in situ studiesnanocrystal growthnanocrystal nucleationpair distribution functionstime-resolved experiments

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Area of Science:

  • Materials Science
  • Nanotechnology
  • Crystallography

Background:

  • In situ and operando pair distribution function (PDF) studies are vital for understanding dynamic processes in materials.
  • Limited synchrotron beam time often hinders thorough investigation of experimental uncertainty and reproducibility in time-resolved total scattering experiments.
  • This restricts the full exploitation of in situ PDF techniques for critical applications like catalysis and energy storage.

Purpose of the Study:

  • To quantify the experimental uncertainty associated with the PDF technique during in situ studies.
  • To assess the impact of user-defined parameters and data processing algorithms on the reliability of time-resolved PDF analysis.
  • To establish best practices for reproducible in situ PDF experiments, focusing on the hydrothermal synthesis of ZrO2 nanoparticles.

Main Methods:

  • Performed in situ pair distribution function (PDF) analysis on the hydrothermal synthesis of ZrO2 nanoparticles.
  • Systematically varied experimental and data processing parameters to evaluate their influence on PDF results.
  • Compared different PDF data processing algorithms to determine their effect on chemical and structural conclusions.

Main Results:

  • User-defined parameters significantly impact the chemical conclusions drawn from time-resolved in situ PDF experiments.
  • Consistent application of identical input parameters across multiple experiments is essential for obtaining comparable and reproducible results.
  • Different PDF processing algorithms can influence the interpretation of chemical analysis, highlighting the need for careful algorithm selection.

Conclusions:

  • Standardizing parameter selection and processing algorithms is critical for enhancing the reliability and reproducibility of in situ PDF studies.
  • This work provides a framework for minimizing uncertainty and maximizing the potential of PDF analysis in dynamic material research.
  • Accurate uncertainty quantification is key to advancing the application of PDF in fields such as nanoparticle synthesis and device operation.