O Função de Erro, often denoted as erf, is a mathematical function that arises frequently in probability, statistics, and partial differential equations describing diffusion processes. It is defined as:
erf(x) = (2/√π) ∫0x e-t² dt
Este integral representa a área sob a curva Gaussiana de 0 a x, effectively measuring the probability that a normally distributed random variable will fall between -∞ and x in the standard distribuição normal.
A Função Erro é particularmente útil em vários campos, incluindo statistics, engineering, and physics, where it helps in the analysis of error rates, processamento de sinais, and thermal diffusion problems. Its complementary function, known as the função erro complementar (erfc), é definida como:
erfc(x) = 1 – erf(x)
Essa função mede a probabilidade de uma variável aleatória Gaussiana exceder um determinado valor.
Em aplicações computacionais, a Função de Erro é frequentemente aproximada usando métodos numéricos or polynomial expansions, especially in machine learning and AI frameworks, where accurate calculations of probabilities are essential for model training and evaluation.