From d8e52d4a1845be892c610198f3081b2d2da14e6a Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Fri, 18 Jun 2021 04:29:39 +0200 Subject: [PATCH] lab4-6 work-in-progress --- podsumowanie/README.md | 137 ++++++++++++++++++++++++++- podsumowanie/lab4/dwumianowy.png | Bin 0 -> 39498 bytes podsumowanie/lab4/dwumianowy2.png | Bin 0 -> 21711 bytes podsumowanie/lab4/inne.png | Bin 0 -> 87351 bytes podsumowanie/lab4/jednostajny.png | Bin 0 -> 21828 bytes podsumowanie/lab4/jednostajny2.png | Bin 0 -> 20473 bytes podsumowanie/lab4/kwantylkwantyl.png | Bin 0 -> 39529 bytes podsumowanie/lab4/normalny.png | Bin 0 -> 92257 bytes podsumowanie/lab4/poissona.png | Bin 0 -> 50733 bytes podsumowanie/lab4/rayleigh.png | Bin 0 -> 41457 bytes podsumowanie/lab4/rayleigh2.png | Bin 0 -> 31539 bytes podsumowanie/lab4/wykladniczy.png | Bin 0 -> 56270 bytes podsumowanie/lab4/wykladniczy2.png | Bin 0 -> 25971 bytes 13 files changed, 132 insertions(+), 5 deletions(-) create mode 100644 podsumowanie/lab4/dwumianowy.png create mode 100644 podsumowanie/lab4/dwumianowy2.png create mode 100644 podsumowanie/lab4/inne.png create mode 100644 podsumowanie/lab4/jednostajny.png create mode 100644 podsumowanie/lab4/jednostajny2.png create mode 100644 podsumowanie/lab4/kwantylkwantyl.png create mode 100644 podsumowanie/lab4/normalny.png create mode 100644 podsumowanie/lab4/poissona.png create mode 100644 podsumowanie/lab4/rayleigh.png create mode 100644 podsumowanie/lab4/rayleigh2.png create mode 100644 podsumowanie/lab4/wykladniczy.png create mode 100644 podsumowanie/lab4/wykladniczy2.png diff --git a/podsumowanie/README.md b/podsumowanie/README.md index b1ee82a..23811bf 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -1,5 +1,7 @@ # Podsumowanie -Podsumowanie zajęć +Podsumowanie zajęć. Zadania z zajęć są na tym repozytorium. [Link](http://wolynski.home.amu.edu.pl/E4BC1/index.html) do strony z wykładami. DSTTLI Hasło: E4BC1 + + --- ## LAB 1 @@ -53,6 +55,7 @@ Lista: ```r # ładowanie danych dane <- read.table("dane1.csv", header = TRUE, sep = ";") +load(url("http://ls.home.amu.edu.pl/data_sets/Centrala.RData")) ankieta <- read.table("http://ls.home.amu.edu.pl/data_sets/ankieta.txt", header = TRUE) computers <- read.csv("http://pp98647.home.amu.edu.pl/wp-content/uploads/2021/06/computers.csv") ``` @@ -111,10 +114,8 @@ Lista: - Dla ujemnych (min -2) wykres jest bardziej spłaszczony niż rozkłąd normalny ![kurtoza](lab3/kurtoza.png) -- **Rozkład empiryczny** - za pomocą szeregu rozdzielczego to np podanie liczebności i udziału procentowego danej zmiennej. - - **Odchylenie standardowe** - intuicyjnie rzecz ujmując, odchylenie standardowe mówi, jak szeroko wartości jakiejś wielkości (na przykład wieku, inflacji, kursu walutowego) są rozrzucone wokół jej średniej. -Im mniejsza wartość odchylenia tym obserwacje są bardziej skupione wokół średniej. +Im mniejsza wartość odchylenia tym obserwacje są bardziej skupione wokół średniej. Odchylenie standardowe z próby ma trochę inny wzór [link](https://pl.wikipedia.org/wiki/Odchylenie_standardowe#Odchylenie_standardowe_z_próby) - **Współczynnik zmienności** - podaje się w procentach, jest to relacja odchylenia standardowego ze średnią. Mówi nam jak bardzo wartości odbiegają od siebie. Dzięki temu ze jest w procentach mozemy porównywać rózne rozkłady. - [Przykład](https://pl.wikipedia.org/wiki/Współczynnik_zmienności) @@ -142,4 +143,130 @@ Kwantyl rzędu 1/2 to inaczej mediana. Kwantyle rzędu 1/4, 2/4, 3/4 są inaczej --- -## LAB 4 \ No newline at end of file +## LAB 4 +Zagadnienia: +- rozkłady statystyczne + +- wykład 3 i 4 na stronie + + + +### R +```r +# 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))) + +barplot(counts, + xlab = "Liczba zgloszen", ylab = "Prawdopodobienstwo", + main = "Rozklady empiryczny i teoretyczny liczby zgloszen", + col = c("red", "blue"), legend = rownames(counts), beside = TRUE) + +#kwanty-kwantyl, linia to moj estymator +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) }) +``` + + +### Rozkłady statystyczne +Jeżeli próbka jest reprezentatywna, to stanowi ona podstawę do wnioskowania o populacji z której pochodzi. Wnioskowanie takie wymaga zbudowania modelu “zachowania się” zmiennej (cechy) X w populacji. Budowa modelu polega na przyjęciu założenia o rozkładzie (teoretycznym) zmiennej X w populacji oraz traktowaniu obserwacji jako wartości tej zmiennej. +

+ +W wykresach na dole to wartość cechy a wysokość słupka to prawdopodobieństwo wystąpienia tej wartości. + +- Dwumianowy +![dwumianowy](lab4/dwumianowy.png) +![dwumianowy2](lab4/dwumianowy2.png) + +- Poissona +![poissona](lab4/poissona.png) + +- Jednostajny +![jednostajny](lab4/jednostajny.png) +![jednostajny2](lab4/jednostajny2.png) + +- Normalny +![normalny](lab4/normalny.png) + +- Wykładniczy +![wykladniczy](lab4/wykladniczy.png) +![wykladniczy2](lab4/wykladniczy2.png) + +- Rayleigha +![rayleigh](lab4/rayleigh.png) +![rayleigh2](lab4/rayleigh2.png) + +- Inne +![inne](lab4/inne.png) + + +### Zagadnienia +- Wykres kwantyl-kwantyl - służy do porównania dwóch rozkładów na podstawie kwantyli. Może służyć do porównania wartości estymowanych z rzeczywistymi. Punkt (x,y) odpowiada jednemu kwantylowi drugiego rodzaju - współrzędna y względem kwantyla tego samego rzędu pierwszego rozkładu - współrzędna x. +![kwantylkwantyl](lab4/kwantylkwantyl.png) + +- Empiryczne - wynikające z doświadczenia + + + +### Estymacja +- estymator + +- estymator nieobciążony + +- Estymatorem największej wiarogodności + +- metody wyznaczania estymatorów + + - Metoda momentów + + - Metoda największej wiarogodności + + - Metoda Monte Carlo + + - Metoda bootstrapowa + + +- Rozkłady estymatorów + + - chi-kwadrat + + - Model wykładniczy + + - Model normalny + + + +--- +## LAB 5 +Zagadnienia: +- przedziały ufności + +- wykład 5 na stronie + + + +### R + + +### Zagadnienia + + + +--- +## LAB 6 +Zagadnienia: +- testy statystyczne, testowanie hipotez statystycznych + +- testy t-studenta + +- wykład 6 i 7 na stronie + + + +### R + + +### Zagadnienia + + diff --git a/podsumowanie/lab4/dwumianowy.png b/podsumowanie/lab4/dwumianowy.png new file mode 100644 index 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