Empirical Distribution of Individuals Formulation

Available identifiers

MaRDI QIDQ6674458

empirical distribution of individuals that follow a medium and influencer

Description

Empirical distribution of individuals that follow a medium 𝑚 and influencer 𝑙 at time 𝑡 by the sum of Dirac delta distributions δ placed at the individuals’ opinions. This distribution describes the stochastic opinion instances at a given time and integrates to ∫ᴰ ρₘ,ₗ⁽ᴺ⁾(𝑥, 𝑡) 𝑑𝑥 ≔ 𝑛ₘ,ₗ⁽ᴺ⁾(𝑡), the proportion of individuals that follow medium 𝑚 and influencer 𝑙.

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Defining Formula: ${\rho }_{m,l}^{(N)}(x,t)=\frac{1}{N}\sum _{\begin{array}{c}i:B_{im}=1\\ C_{il}(t)=1\end{array}}\delta (x-x_i(t))$

$B_{i}m$ symbol represents Medium Follower Matrix

$C_{i}m$ symbol represents Influencer Individual Matrix

$N$ symbol represents Total Number of Individuals

$\delta$ symbol represents Dirac Delta Distribution

${\rho }_{m,l}^{(N)}$ symbol represents Empirical Distribution of Individuals

$t$ symbol represents Time

$x$ symbol represents Opinion

$x_i$ symbol represents Opinion

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