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Intervalos de Confianza
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2ª Parte Tema 10Estimación por Intervalos
, Inferencia Estadística
La Inferencia es un proceso mediante el cual, a partir de la información
obtenida en una muestra, extraemos conclusiones sobre una población.
X=Variable poblacional de interés ~ F(x, θ),
θ parámetro fijo desconocido.
POBLACIÓN
I1,…,In (n individuos)
INFERENCIA
Muestra m.a.s.
(X1, X2,…,Xn )
Datos (x1, x2,…,xn ) n-observaciones
Xi ~ X , i = 1,…,n
Independientes
, ¿Cómo se puede Inferir?
Sea X ~ F(x, θ), siendo θ un parámetro desconocido.
Elegimos una m.a.s. (X1, X2,…,Xn )
Estimación Puntual
Estimación
Inferencia Estimación por Intervalos
Contrastes de Hipótesis
, Intervalos de confianza (IC)
Hasta el momento: X ~ F(x, θ), siendo θ un parámetro desconocido
(x1, x2,…,xn) m.a.s.
estimación puntual de θ
θ̂ θ̂ (x 1 ,..., x n ) (valor numérico concreto)
Ejemplo: X = Nº averías mensuales de una máquina
µ = E[X] parámetro a estimar
Dada (x1, x2, x3, x4) m.a.s.
Objetivo x1 x2 x3 x4 obtener una estimación de
y ˆ X 4
(2,3,1,2) ˆ1 2 averías
(2,1,0,2) ˆ 2 5 4 1.25 averías
(4,1,1,3) ˆ 3 9 4 2.25 averías
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