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Identification of Alternative Splicing and Polyadenylation in RNA-seq Data
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An alternative to the Cauchy distribution.

Ayman Alzaatreh1

  • 1Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates.

Methodsx
|August 2, 2019
PubMed
Summary
This summary is machine-generated.

A novel exponentiated-exponential Cauchy distribution (EECD) is introduced, offering greater flexibility than the standard Cauchy distribution. This new distribution allows for defined moments and a wide range of skewness and kurtosis values.

Keywords:
Cauchy distributionEstimationExponentiated-exponential-X familyMomentsShannon entropyT-X familyThe paper proposes an alternative to the Cauchy distribution using the T-X family framework proposed by Alzaatreh et al. (2013). The proposed distribution can be left skewed, right skewed or symmetric. The moments are defined under some restriction on the parameter space

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • Generalizations of the Cauchy distribution are explored in statistical literature.
  • Existing Cauchy distribution lacks defined moments and has limited flexibility.

Purpose of the Study:

  • To propose a new generalization of the Cauchy distribution, the exponentiated-exponential Cauchy distribution (EECD).
  • To investigate the mathematical properties and estimation methods for the proposed EECD.

Main Methods:

  • Introduction of the exponentiated-exponential Cauchy distribution (EECD).
  • Analysis of the distribution's characteristics, including moments, skewness, and kurtosis.
  • Study of two distinct parameter estimation methods for EECD.

Main Results:

  • The EECD possesses a closed-form cumulative distribution function.
  • EECD exhibits flexible shape characteristics, accommodating left-skewed, right-skewed, and symmetric data.
  • Moments for the EECD are defined within specific parameter constraints, unlike the standard Cauchy distribution.

Conclusions:

  • The exponentiated-exponential Cauchy distribution (EECD) offers a flexible and valuable addition to the family of Cauchy-related distributions.
  • EECD provides a broader range of statistical modeling capabilities due to its adaptable shape and defined moments.