The books of the continuous Bernoulli distribution

[meiyulee]

Continuous Bernoulli distribution can help the researchers transferring the discrete states to the continuous states in artificial intelligence and achieving accurate computations and predictions.

This github is for the first book of the continuous Bernoulli distribution to show (1) the statistical inference including the sufficient statistic, the point estimator, the interval estimation, the test statistic, the goodness of fit, and the one-way analysis. (2) the continuous binomial distribution, (3) the continuous trinomial distribution.

We also verified that
(1) the special Beta distribution and compared it with the continuous Bernoulli distribution.
(2) how about the continuous Bernoulli distribution and the continuous binomial distribution as λ ->0.
We also built the four models to solve the case of k categories.

The four books can be downloaded at vixra.org or researchgate.

[meiyulee]

Book series

• Continuous Bernoulli Distribution-Simulator and Test Statistic. https://vixra.org/abs/2012.0088

• The Continuous Bernoulli Approaching Distribution When λ → 0 and the Continuous Binomial Distribution. https://vixra.org/abs/2012.0221

• Multi Categories Analytic Method Using Continuous Bernoulli Distribution and Conditional Distribution. https://vixra.org/abs/2101.0034

• Special Beta Distribution for Big Data Analysis: X ~ Beta (α = λ + 1, β = 2 – λ). https://vixra.org/abs/2101.0082

[varelajosericardo]

Hi. Thanks for your contribution.
Could it be that the variance has a small error in the publications tough?
If I compute the variance for a lambda parameter of 0.75 the formula ((1-L)L)/((1-2L)^2)+1/((2atanh(1-2L)^2) will return 1.598, if I add a "-" sign at the beginning of the formula it results -((1-L)L)/((1-2L)^2)+1/((2atanh(1-2L)^2) it will return a correct 0.0785.
Also at 0,5 it will be 1/12=0.08333......
Testing the publish formula with 0,5001 (it should be close to 0.08333) it returns 124999.58. The corrected formula above yields 0.0833332669644733