Aggregating a Group of Agents: Sum of Powers
Explore the aggregation of fluctuating agents, focusing on variance relations and quantile analysis.
Explore the aggregation of fluctuating agents, focusing on variance relations and quantile analysis.
Explore the technical details of log-normal and log-Laplace distributions, including moments and variance calculations.
Explore the relationship between variance and population size using a power law model, focusing on the implications for aggregate and part populations.
Explore Mandelbrot's insights on the sensitivity of size distributions, particularly focusing on the lognormal distribution and its implications.
Explore the estimation of moments for logarithms of aggregate sales using Taylor expansion, focusing on expected value and variance.
Explore the derivation of value distribution from population distribution using a log-normal model, emphasizing its application in size distribution analysis.
Explore the mathematical derivation and properties of moments in a log-Laplace distribution, including detailed equations and theoretical insights.
Explore the origin of departure from the Law of Large Numbers in agent populations, examining firm comovement and self-variance.
Explore the decomposition of sectoral sales time series into components, focusing on aggregate variance and cross covariance matrices.
Explore various similarity measures such as Pearson correlation, cosine similarity, and covariance to understand relationships within data matrices.
Explore the impact of comovements and variance in large numbers, focusing on the balance between self-variance and covariance among agents.
Explore the variance of time series means in quantile levels, examining the law of large numbers and its implications on aggregate statistics.