From c180a99a2e49daebe29c973a24f8c8498cd46507 Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Fri, 18 Jun 2021 11:25:55 +0200 Subject: [PATCH] lab4 done --- podsumowanie/README.md | 54 ++++++++++++++++++++------ podsumowanie/lab4/bootstrap.png | Bin 0 -> 106485 bytes podsumowanie/lab4/chi.png | Bin 0 -> 40179 bytes podsumowanie/lab4/enormalny.png | Bin 0 -> 62728 bytes podsumowanie/lab4/ewykladniczy.png | Bin 0 -> 46741 bytes podsumowanie/lab4/mc1.png | Bin 0 -> 53760 bytes podsumowanie/lab4/mc2.png | Bin 0 -> 71649 bytes podsumowanie/lab4/metodamomentow.png | Bin 0 -> 61205 bytes podsumowanie/lab4/metodamomentow2.png | Bin 0 -> 46992 bytes podsumowanie/lab4/moment.png | Bin 0 -> 46037 bytes podsumowanie/lab4/nw.png | Bin 0 -> 74684 bytes zajecia4/README.md | 2 +- zajecia4/zadania.R | 2 +- 13 files changed, 44 insertions(+), 14 deletions(-) create mode 100644 podsumowanie/lab4/bootstrap.png create mode 100644 podsumowanie/lab4/chi.png create mode 100644 podsumowanie/lab4/enormalny.png create mode 100644 podsumowanie/lab4/ewykladniczy.png create mode 100644 podsumowanie/lab4/mc1.png create mode 100644 podsumowanie/lab4/mc2.png create mode 100644 podsumowanie/lab4/metodamomentow.png create mode 100644 podsumowanie/lab4/metodamomentow2.png create mode 100644 podsumowanie/lab4/moment.png create mode 100644 podsumowanie/lab4/nw.png diff --git a/podsumowanie/README.md b/podsumowanie/README.md index f0aafd1..f4029e5 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -167,6 +167,24 @@ qqplot(rpois(length(Centrala$Liczba), lambda = lambda_est), Centrala$Liczba, xlab = "Kwantyle teoretyczne", ylab = "Kwantyle empiryczne", main = "Wykres kwantyl-kwantyl dla liczby zgloszen") qqline(Centrala$Liczba, distribution = function(probs) { qpois(probs, lambda = lambda_est) }) + +# odchylenie standardowe dla próby to musimy dodatkowo pomnozyc przez ten pierwiastek na koncu!!! +a_est_mm <- mean(czas_oczek_tramwaj) - + sqrt(3) * sd(czas_oczek_tramwaj) * sqrt((length(czas_oczek_tramwaj) - 1) / (length(czas_oczek_tramwaj))) +b_est_mm<- mean(czas_oczek_tramwaj) + + sqrt(3) * sd(czas_oczek_tramwaj) * sqrt((length(czas_oczek_tramwaj) - 1) / (length(czas_oczek_tramwaj))) + +# metoda największej warygodności +a_est <- min(czas_oczek_tramwaj) +b_est <- max(czas_oczek_tramwaj) + +# metoda najwiekszej warygodnosci +curve(dunif(x, a_est, b_est), + add = TRUE, col = "blue", lwd = 2) + +#metoda momentów +curve(dunif(x, a_est_mm, b_est_mm), + add = TRUE, col = "green", lwd = 2) ``` @@ -211,31 +229,43 @@ W wykresach na dole to wartość cechy a wysokość słupka to prawdopodobieńst ### Estymacja -- estymator +- Estymator - statystyka (funkcja mierzalna określona na przestrzeni statystycznej) służąca do szacowania wartości parametru rozkładu. -- estymator nieobciążony +- Estymator nieobciążony - wartość oczekiwana rozkładu estymatora jest równa wartości szacowanego parametru. -- Estymatorem największej wiarogodności +- Moment - moment zwykły rzędu k zmiennej losowej to wartość oczekiwana k-tej potęgi tej zmiennej. + - zmienna losowa to funkcja prawdopodobieństwa + - wartość oczekiwana to wartość określająca spodziewany wynik doświadczenia losowego. Dobrym estymatorem wartości oczekiwanej jest średnia. +![moment](lab4/moment.png) -- metody wyznaczania estymatorów +- Metody wyznaczania estymatorów: - - Metoda momentów + - Metoda momentów. Zwykle momenty uk są funkcjami parametrów. Tworzymy układ równań uk = estymator momentu
+ ![metodamomentow](lab4/metodamomentow.png) + ![metodamomentow2](lab4/metodamomentow2.png) - - Metoda największej wiarogodności + - Metoda największej wiarogodności
+ ![nw](lab4/nw.png) - - Metoda Monte Carlo + - Metoda Monte Carlo - losowanie, porównywanie
+ ![mc1](lab4/mc1.png) + ![mc2](lab4/mc2.png) + + - Metoda bootstrapowa - mamy jakąś próbę z n obeserwacjami i z tej próby losujemy elementy - uzyskujemy próbkę bootstrapową. Powtarzając ten proces otrzymujemy ciąg próbek i odpowiadających jej wartości statystyki. Dzięki tej metodzie, wyniki testów parametrycznych i analiz opartych o modele liniowe są bardziej precyzyjne. Metoda szacowania (estymacji) wyników poprzez wielokrotne losowanie ze zwracaniem z próby. Przydatna gdy nie znamy typu rozkładu. + ![bootstrap](lab4/bootstrap.png) - - Metoda bootstrapowa - Rozkłady estymatorów - - chi-kwadrat + - chi-kwadrat - rozkład zmiennej losowej, która jest sumą k kwadratów niezależnych zmiennych losowych o standardowym rozkładzie normalnym.
+ ![chi](lab4/chi.png) - - Model wykładniczy - - - Model normalny + - Model wykładniczy
+ ![ewykladniczy](lab4/ewykladniczy.png) + - Model normalny
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zt|jcE?SFONe|6z;aF;xG?i@4!(@6g=g!jO~=|z!eH~g181KkYZ{!OTc===WNjs8`~ zXJ5kMQobqgx6%CPuK0JM`f)Uv5{#>9UH)e?9DPBfz*^(W3C3UN=uZC6D^3D@mj4f) b^fi7}D*5_14qG-1@J~Zk8&Rfg5%B*2jFfqS literal 0 HcmV?d00001 diff --git a/zajecia4/README.md b/zajecia4/README.md index 22fbb2b..58b923c 100644 --- a/zajecia4/README.md +++ b/zajecia4/README.md @@ -39,7 +39,7 @@ Metoda momentów – w statystyce, metoda estymacji parametrów populacji polega ## Moment Moment zwykły rzędu k zmiennej losowej to wartość oczekiwana k-tej potęgi tej zmiennej. - zmienna losowa to funkcja prawdopodobieństwa - - wartość oczekiwana to prawdopodobieństwo dla x razy wartość x. Dobrym estymatorem wartości oczekiwanej jest średnia. + - wartość oczekiwana to wartość określająca spodziewany wynik doświadczenia losowego. Dobrym estymatorem wartości oczekiwanej jest średnia. ## Próba diff --git a/zajecia4/zadania.R b/zajecia4/zadania.R index 3705387..af51e8d 100644 --- a/zajecia4/zadania.R +++ b/zajecia4/zadania.R @@ -9,7 +9,7 @@ a_est_mm <- mean(czas_oczek_tramwaj) - b_est_mm<- mean(czas_oczek_tramwaj) + sqrt(3) * sd(czas_oczek_tramwaj) * sqrt((length(czas_oczek_tramwaj) - 1) / (length(czas_oczek_tramwaj))) -# metona największej warygodności +# metoda największej warygodności a_est <- min(czas_oczek_tramwaj) b_est <- max(czas_oczek_tramwaj)