Statistics

    

Special Beta Distribution for Big Data Analysis: X ~ Beta (α = λ + 1, β = 2 – λ)

Authors: Kuan-Shian Wang, Mei-Yu Lee

This book discusses the special case of Beta distribution as α = λ + 1 and β = 2 – λ. To compare with the continuous Bernoulli distribution, the change of λ affected the pdf of the special Beta distribution. Then find out the sufficient statistic, the point estimator, the confidence interval, the test statistic, and the goodness of fit. The special Beta distribution at the case of λ = 0.5 is different from the continuous Bernoulli distribution. The special Beta distribution pdf is changed in smoothing but the Continuous Bernoulli distribution pdf has a big wave when λ is from small to large. As the sample size becomes large, two distributions are approximated to Normal distribution with different relationships between λ and the sum of samples.

Comments: 89 Pages. [Corrections made to conform with the requirements on the Submission Form]

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[v1] 2021-01-13 14:07:54

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