14 docs tagged with "mathematics"

Explore the technical details of log-normal and log-Laplace distributions, including moments and variance calculations.

Explore the mathematical formulation of cosine similarity between industries using areal employment data, and compare discrete and continuous approaches.

Explore the relationship between variance and population size using a power law model, focusing on the implications for aggregate and part populations.

Explore the formal model for estimating pLQ and understand the propagation of volatility in log(scp) to log(LQ).

Explore Mandelbrot's insights on the sensitivity of size distributions, particularly focusing on the lognormal distribution and its implications.

Explore the mathematical framework for understanding aggregate volatility in log scale, focusing on variance and covariance among agents.

An overview of the relationships between micro and macro fluctuations in linear and log terms, with a focus on differences and variances.

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 implications of logarithmic transformations in economic fluctuations, focusing on nonlinearities and their practical applications.

Explore the normalization techniques in industry coexistence and the solution for industry self-overlap, incorporating Gaussian and Laplace density functions.

Explore the two-dimensional distribution of growth rates in the LQ problem and the implications for volatility and growth probabilities.

A detailed overview of the sections covering literature review, data methods, mathematical definitions, and the core contributions related to aggregation of micro volatility.

Explore the impact of comovements and variance in large numbers, focusing on the balance between self-variance and covariance among agents.