From 6800644021876176de4ed46b19d263bd829f5ede Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Fri, 18 Jun 2021 23:03:47 +0200 Subject: [PATCH] lab5 --- podsumowanie/README.md | 60 ++++++++++++++++++++++++++++++++ podsumowanie/lab5/bootstrap.png | Bin 0 -> 65672 bytes podsumowanie/lab5/inne.png | Bin 0 -> 55188 bytes podsumowanie/lab5/student.png | Bin 0 -> 59856 bytes podsumowanie/lab5/ufnosc.png | Bin 0 -> 52083 bytes zajecia5/README.md | 2 +- 6 files changed, 61 insertions(+), 1 deletion(-) create mode 100644 podsumowanie/lab5/bootstrap.png create mode 100644 podsumowanie/lab5/inne.png create mode 100644 podsumowanie/lab5/student.png create mode 100644 podsumowanie/lab5/ufnosc.png diff --git a/podsumowanie/README.md b/podsumowanie/README.md index e1898b0..ea0ebdf 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -185,6 +185,21 @@ curve(dunif(x, a_est, b_est), #metoda momentów curve(dunif(x, a_est_mm, b_est_mm), add = TRUE, col = "green", lwd = 2) + +# bootstrap +library(boot) +dane <- rnorm(100) +meanboot <- function(x,i)mean(x[i]) +bmean=boot(dane,meanboot,1000) +hist(bmean$t-mean(dane),prob=T,main='') +curve(dnorm(x,0,1/sqrt(length(dane))),add=T,col='red') + +# monte carlo +dane <- rnorm(100) +mcmean <- vector('numeric',1000) +for(i in 1:1000) mcmean[i] <- mean(rnorm(100)) +hist(mcmean,prob=T,main='') +curve(dnorm(x,0,0.1),add=T,col='red') ``` @@ -226,6 +241,8 @@ W wykresach na dole to wartość cechy a wysokość słupka to prawdopodobieńst - Empiryczne - wynikające z doświadczenia +- Próba statystyczna – zbiór obserwacji statystycznych wybranych (zwykle wylosowanych) z populacji. + ### Estymacja @@ -278,9 +295,52 @@ Zagadnienia: ### R +```r +# klasyczne przedziały ufności +library(EnvStats) +epois(Centrala$Liczba, + method = "mle/mme/mvue", + ci = TRUE, ci.type = "two-sided", conf.level = 0.95, + ci.method = "exact")$interval$limits +eexp(Czas,ci=T) + +# klasyczne przedziały ufności +load("Awarie.RData") +attach(Awarie) +m <- mean(Czas) +n <- length(Czas) +a <- 0.05 +L <- qchisq(a/2,2*n)/(2*n*m) +R <- qchisq(1-(a/2),2*n)/(2*n*m) + +# bootstrapowe przedziały ufności +library(boot) +load("Awarie.RData") +attach(Awarie) +lambdaboot <- function(x,i) 1/mean(x[i]) +blambda <- boot(Czas,lambdaboot,1000) +boot.ci(blambda,conf=0.95,type='perc') +``` ### Zagadnienia +- Estymacja przedziałowa - np jakieś urządzenie moze działać na pewnym przedziale wartości. + +- Chcemy "złapać" jakąś wartość w przedział. Jest to lepsze niz próba oszacowania dokładnej wartości. +Jeżeli konstruujemy jakiś przedział z poziomem ufności 0,95 to na 100 prób w 95 nasz parametr jest w przedziale. + +- Na podstawie funkcji centralnej mozemy stworzyć przedziały ufności. Funkcję centralną bierzemy z tabelki. +Podstawiamy funkcję centralną do prawdopodobieństwa oraz 1-a, wsadzamy parametr pomiędzy funkcję i wyliczamy a i b. a i b to przedział ufności. Jest przykład w pdfie w labach 5.
+![ufnosc](lab5/ufnosc.png) + +- Rozkład t-Studenta - kolejny typ rozkładu. Podobny to rozkładu normalnego.
+![student](lab5/student.png) + +- Dodatkowe
+![inne](lab5/inne.png) + +- Bootstrapowe przedziały ufności - po prostu przedział ufności z próbki bootstrapowej. (Z niewielkiej próby tworzymy losując ze zwracaniem zestaw wielu prób)
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