Empirical Distribution of Individuals Formulation
type: Item
instance of: mathematical expression
instance of: dimensionless expression
in defining formula: B i m
in defining formula: C i m
in defining formula: N
in defining formula: δ
in defining formula: ρ m , l ( N )
in defining formula: t
in defining formula: x
in defining formula: x i
specialized by: Limiting Distribution of Individuals Formulation
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.
community: MathModDB
MaRDI profile type: MaRDI formula profile
defining formula: ρ m , l ( N ) ( x , t ) = 1 N ∑ i : B i m = 1 C i l ( t ) = 1 δ ( x − x i ( t ) )
description: empirical distribution of individuals that follow a medium and influencer