# Economic Segregation Under the Action of Trading Uncertainties

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## Abstract

**:**

## 1. Introduction

## 2. A Brief Excursion on Kinetic Modeling of Opinion Formation

## 3. Kinetic Modeling of Uncertain Trading Activity

**Remark**

**1.**

**Remark**

**2.**

**Remark**

**3.**

## 4. Statistical Study of the Marginal Wealth Distribution

#### 4.1. Literature Approaches

#### 4.2. Bayesian Approach

## 5. Numerical Results Based on Markov Chain Monte Carlo

#### 5.1. Estimation of the Marginal Function

- The support was shifted by 0.3 (which in the case of the function (27) is the value of the parameter $\delta $).
- The support was multiplied by a factor equal to 10 to highlight the shape of the wealth distribution.

#### 5.2. Estimation of the Posterior Function

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Beta probability distribution functions plotted for different values of parameters $\alpha $ and $\beta $.(

**b**) marginal distribution functions computed for each of the Beta distributions.

**Figure 2.**We report the sensitivity analysis on the marginal distribution in (

**b**) performed for different parameters of the Beta distribution in (

**a**) obtained for the length of the support fixed to five.

**Figure 3.**Sensitivity analysis performed on different values of the length of the support using a Beta density function with $\alpha =0.1,\beta =0.1$ as the opinion distribution.

**Figure 5.**Posterior estimation through Metropolis–Hastings for different prior distributions: (

**a**) Beta distribution with parameters $\alpha =0.1$ and $\beta =0.1$, (

**b**) Beta distribution with parameters $\alpha =3$ and $\beta =3$, (

**c**) Beta distribution with parameters $\alpha =2$ and $\beta =8$, (

**d**) Beta distribution with parameters $\alpha =8$ and $\beta =2$.

**Table 1.**Gini index for each inverse Gamma distribution derived from the corresponding Beta distribution with parameters shown in the legend.

Prior Parameters | Gini Index |
---|---|

$\alpha =0.1$, $\beta =0.1$ | 0.55 |

$\alpha =3$, $\beta =3$ | 0.61 |

$\alpha =2$, $\beta =8$ | 0.56 |

$\alpha =8$, $\beta =2$ | 0.67 |

**Table 2.**Estimation of the posterior parameters of the Beta distribution fixing the prior distribution.

Prior Parameters | Posterior Parameters |
---|---|

$\alpha =0.1$, $\beta =0.1$ | $\widehat{\alpha}=0.41$, $\widehat{\beta}=0.22$ |

$\alpha =3$, $\beta =3$ | $\widehat{\alpha}=3.41$, $\widehat{\beta}=3.17$ |

$\alpha =2$, $\beta =8$ | $\widehat{\alpha}=2.62$, $\widehat{\beta}=8.33$ |

$\alpha =8$, $\beta =2$ | $\widehat{\alpha}=8.28$, $\widehat{\beta}=2.23$ |

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**MDPI and ACS Style**

Ballante, E.; Bardelli, C.; Zanella, M.; Figini, S.; Toscani, G. Economic Segregation Under the Action of Trading Uncertainties. *Symmetry* **2020**, *12*, 1390.
https://doi.org/10.3390/sym12091390

**AMA Style**

Ballante E, Bardelli C, Zanella M, Figini S, Toscani G. Economic Segregation Under the Action of Trading Uncertainties. *Symmetry*. 2020; 12(9):1390.
https://doi.org/10.3390/sym12091390

**Chicago/Turabian Style**

Ballante, Elena, Chiara Bardelli, Mattia Zanella, Silvia Figini, and Giuseppe Toscani. 2020. "Economic Segregation Under the Action of Trading Uncertainties" *Symmetry* 12, no. 9: 1390.
https://doi.org/10.3390/sym12091390