Statistics

2101 Submissions

[3] viXra:2101.0082 [pdf] submitted on 2021-01-13 14:07:54

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

Authors: Kuan-Shian Wang, Mei-Yu Lee
Comments: 89 Pages. [Corrections made to conform with the requirements on the Submission Form]

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.
Category: Statistics

[2] viXra:2101.0046 [pdf] submitted on 2021-01-06 17:52:45

Analyzing the Side Force on a Baseball Using Hawk-Eye Measurements

Authors: Glenn Healey, Lequan Wang
Comments: 19 Pages.

We use Hawk-Eye measurements to analyze the side force on a baseball.
Category: Statistics

[1] viXra:2101.0034 [pdf] submitted on 2021-01-05 09:18:19

Multi Categories Analytic Method Using Continuous Bernoulli Distribution and Conditional Distribution

Authors: Kuan-Shian Wang, Mei-Yu Lee
Comments: 195 Pages.

This book provides four model designs to discuss how continuous Bernoulli distribution extends to the analysis of K categories. By contrast to the discrete polynomial distribution which is extended from Bernoulli distribution depending on the additive property, the random variable of continuous Bernoulli should be tested the pdf, cdf, distribution, and checked if maintain the characteristics of CB distribution or not. Model 1 is from random variable method(variable-added), Model 2 and 3 are from the probability model-building and suitable for the parameter-added or the conditional relationship of variables, respectively. Model 4 is from the continuous trinomial distribution and suitable for the joint relationship of variables.
Category: Statistics