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Observation and Analysis of Blinking Surface-enhanced Raman Scattering
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An one-parameter compounding discrete distribution.

Emrah Altun1, Gauss M Cordeiro2, Miroslav M Ristić3

  • 1Department of Mathematics, Bartin University, Bartin, Turkey.

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Summary
This summary is machine-generated.

Researchers introduced a new discrete distribution by combining Poisson and xgamma distributions. This novel distribution offers new tools for statistical analysis and modeling count data.

Keywords:
62E15Discrete distributionPoisson distributioncompoundingxgamma distribution

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • Discrete distributions are fundamental in statistical modeling.
  • Existing distributions may not capture all complex count data patterns.
  • The Poisson and xgamma distributions are well-established but have limitations.

Purpose of the Study:

  • To propose a new one-parameter discrete distribution by compounding Poisson and xgamma distributions.
  • To investigate the statistical properties of this novel distribution.
  • To introduce count regression and integer-valued autoregressive models based on the new distribution.

Main Methods:

  • Compounding the Poisson and xgamma distributions.
  • Derivation of statistical properties: moments, probability generating functions, and moment generating functions.
  • Parameter estimation using Maximum Likelihood Estimation (MLE) and Method of Moments (MOM).
  • Development of count regression and integer-valued autoregressive (IVAR) models.

Main Results:

  • A new one-parameter discrete distribution was successfully derived.
  • Key statistical properties, including generating functions, were determined.
  • The proposed distribution was shown to be estimable using MLE and MOM.
  • Count regression and IVAR models were formulated using the new distribution.

Conclusions:

  • The new compound discrete distribution offers a flexible alternative for modeling count data.
  • The derived statistical properties and estimation methods provide a foundation for its application.
  • The introduced count regression and IVAR models extend its utility to time series and regression analyses.