Distribución Gamma
La Distribución Gamma es una familia de funciones de densidad continua de dos parámetros distribuciones de probabilidad. It is defined by a shape parameter (k) and a scale parameter (θ). The probability (PDF) de la Distribución Gamma se expresa como:
f(x; k, θ) = (1 / (θ^k * Γ(k))) * x^(k-1) * e^(-x/θ), for x > 0, k > 0, and θ > 0, where Γ(k) is the gamma function evaluated at k.
Esta distribución es particularmente útil en diversos campos como statistics, queuing models, and aprendizaje automático, where it often models waiting times or lifetimes of objects. The Gamma Distribution encompasses several well-known distributions: when k is a positive integer, it becomes the Erlang distribution, and when k = 1, it simplifies to the distribución exponencial.
In practical applications, the shape parameter influences the skewness of the distribution, while the scale parameter stretches or compresses the distribution along the x-axis. The mean of the Gamma Distribution is given by μ = k * θ, and the variance is σ² = k * θ².
En aprendizaje automático, la Distribución Gamma puede ser utilizada en inferencia bayesiana and for modeling uncertainty. Its ability to express a wide range of shapes makes it a flexible choice for various modelado de datos escenarios.