Lottery 3D Analysis 福彩3D分析

1. 介绍

彩票市场在中国内地甚至全球的市场占有份额日益增加，越来越多赌徒热爱购买彩票。今天僕尝试分析随机内地彩票---福彩3D为数据，分析是否可能从中获利。

2. 读取数据

福彩3D: 直选走势数据从2016158期至2017158期，一共有360个观测数据。该福彩类型规则乃预测3个随机数字，从000至999。

3. 数学模式

• kfoots：kfoots程序包使用马克夫链，举例此期开彩010，该模式将分析及预测每当开彩该成绩后的下一个成绩（状态的转换率）的机率
• PoisNor：PoisNor程序包提供多随机变量产生器及相关系数分析
• poilog：poilog程序包分析双变量泊松模式
• mvrpois：mvrpois程序包分析多变量泊松模式

在此，僕使用mvrpois多变量泊松模式分析仨变量泊松3D彩票数据，有关详情请查阅Dimitris Karlis and Loukia Meligkotsidou (2005)^[7.3 参考文献中的4th文献]和Dimitris Karlis (2002)^[7.3 参考文献中的3rd文献]。

$$(X_{1},X_{2},X_{3}){i} ~ 3 - Pois(\theta{1i},\theta_{2i},\theta_{3i},\theta_{12i},\theta_{13i},\theta_{23i}) \dots equation\ 3.1$$

• $log(\theta_{1i}) = \alpha_{1} + \beta_{1}z_{i}$
• $log(\theta_{2i}) = \alpha_{2} + \beta_{2}z_{i}$
• $log(\theta_{3i}) = \alpha_{3} + \beta_{3}z_{i}$
• $log(\theta_{12i}) = \alpha_{4} + \beta_{4}z_{i}$
• $log(\theta_{13i}) = \alpha_{5} + \beta_{5}z_{i}$
• $log(\theta_{23i}) = \alpha_{6} + \beta_{6}z_{i}$

联合分布函数将为：

$$P(X = x) = \sum_{(y_{12},y_{13},y_{23})\in C}\frac{exp(-\sum\theta_{i})\theta_{1}^{x_{1}-y_{12}-y_{13}}\theta_{2}^{x_{2}-y_{12}-y_{23}}\theta_{3}^{x_{3}-y_{13}-y_{23}}\theta_{12}^{y_{12}}\theta_{13}^{y_{13}}\theta_{23}^{y_{23}}}{(x_{1}-y_{12}-y{13})!(x_{2}-y_{12}-y{23})!(x_{3}-y_{13}-y{23})!y_{12}!y_{13}!y_{23}!} \dots equation\ 3.2$$ 而 $C \subset N^3$ 设为：

$$C = (y_{12},y_{13},y_{23}) \in N^3 : {y_{12}+y_{13}\leq x_{1}} \cup {y_{12}+y_{23}\leq x_{2}} \cup {y_{13}+y_{23}\leq x_{3}} \neq \theta$$

**Rerefences for multivariate Poisson models : **

• Can a Multivariate Poisson Distribution be implemented in Stan?
• n-mixture model in Stan? marginalizing
• karlis-ntzoufras-reproduction/model.stan
• Reproductions of models for football (soccer) matches in Stan/PyStan^[So far, the following models have been implemented:] ^[1) Maher (1982) - Modelling Association Football Scores - maher] ^[2) Dixon and Coles (1997) - Modelling Association Football Scores and Inefficiencies in the Football Betting Market - dixon-coles] ^[3)Karlis and Ntzoufras (2008) - Bayesian modelling of football outcomes (using the Skellam's distribution) - karlis-ntzoufras]

4. 投注模式

由于凯利投资模式，在此使用该模式。有关凯利模式投注，请参阅：

• Application of Kelly Criterion model in Sportsbook Investment
• Job Application - Quantitative Analyst (binary.com)

5. 盈利

6. 结论

7. 附录

7.1 文献明细

It's useful to record some information about how your file was created.

• File creation date: 2017-06-15
• File latest updated date: r Sys.Date()
• r R.version.string
• R version (short form): r getRversion()
• rmarkdown package version: r packageVersion('rmarkdown')
• tint package version: r packageVersion('tint')
• File version: 1.0.0
• Author Profile: ®γσ, Eng Lian Hu
• GitHub: Source Code
• Additional session information

7.2 版本

• 文献版本: 1.0.0 - "2017-06-15 20:47:50 JST"

7.3 参考文献

1. Bayesian Multivariate Poisson Regression for Models of Injury Count, by Severity by Jianming Ma and Kara M. Kockelman (2006)
2. FlexMix - An R package for finite mixture modelling by Bettina Grun and Friedrich Leisch (2007)
3. Multivariate Poisson Models by Dimitris Karlis (2002)
4. Multivariate Poisson Regression with Covariance Structure (Preview) by Dimitris Karlis and Loukia Meligkotsidou (2005)
5. Package 'poilog' by Vidar Grøtan and Steinar Engen (2015)
6. Resampling Methods for Longitudinal Data Analysis by Yue Li (2005)

7.4 感言