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Intervalos de Confianza

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  • March 14, 2022
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  • 2022/2023
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2ª Parte Tema 10
Estimación 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
4

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