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Equal-bin-width histogram versus equal-bin-count histogram.

Piotr Sulewski1

  • 1Institute of Mathematics, The Pomeranian University, Słupsk, Poland.

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|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces two novel histogram methods: equal bin width (EBWH) and equal bin count (EBCH). It optimizes parameters for both methods using Monte Carlo simulations to maximize data similarity.

Keywords:
62G0762G30Empirical density functionMonte Carlo simulationhistogramrandom number generatorsimilarity measure

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Area of Science:

  • Statistics
  • Data Visualization
  • Computational Methods

Background:

  • Traditional histograms use fixed bin widths, leading to random bin counts.
  • This research proposes a converse approach with fixed bin counts, resulting in variable bin widths.

Purpose of the Study:

  • Optimize parameter selection for equal bin width (EBWH) and equal bin count (EBCH) histograms.
  • Evaluate similarity measures between empirical and theoretical data for both methods.
  • Conduct a comparative analysis of EBWH and EBCH using frequency formulas.

Main Methods:

  • Monte Carlo simulations to determine optimal bin width in EBWH.
  • Monte Carlo simulations to determine optimal bin count in EBCH.
  • Development of similarity measures and frequency formulas for comparative analysis.

Main Results:

  • Identified optimal constant bin width for EBWH maximizing similarity.
  • Identified optimal constant bin count for EBCH maximizing similarity.
  • Presented similarity measures and comparative analysis results for both histogram types.

Conclusions:

  • Both EBWH and EBCH offer distinct advantages for data representation.
  • The study provides practical guidance for implementing EBCH, including handling non-divisible data.
  • Accompanying Mathcad software facilitates the application of both novel histogram methods.