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restructured file organisation and finished assignment 2a

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Christopher Sanden
2026-03-12 16:36:50 +01:00
parent d4154cd83d
commit f285b06064
44 changed files with 1019 additions and 0 deletions
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Oblig/1a/Coop_raw_98.xlsx Normal file
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Oblig/1a/FrekvensCoop.csv Normal file
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Lengde,n
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Oblig/1a/FrekvensLaban.csv Normal file
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Version: 1.0
RestoreWorkspace: Default
SaveWorkspace: Default
AlwaysSaveHistory: Default
EnableCodeIndexing: Yes
UseSpacesForTab: Yes
NumSpacesForTab: 2
Encoding: UTF-8
RnwWeave: Sweave
LaTeX: pdfLaTeX

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library(readxl)
library(dplyr)
library(ggplot2)
laban <- read_excel("Laban_raw_98.xlsx")
coop <- read_excel("Coop_raw_98.xlsx")
#Finner kolonne-navn
names(laban)
names(coop)
#Frekvenser
freq_laban <- laban %>%
count(Lengde) %>%
arrange(Lengde)
#Velger å trekke fra de tre første radene i coop tabellen
#Gjør dette for å få et mer representativt bilde av dataen
#De tre første strekkene var ikke like metode som resten
freq_coop <- coop %>%
slice(4:n()) %>%
count(Lengde) %>%
arrange(Lengde)
freq_laban
freq_coop
write.csv(freq_laban, "FrekvensLaban.csv", row.names = FALSE, quote = FALSE)
write.csv(freq_coop, "FrekvensCoop.csv", row.names = FALSE, quote = FALSE)
#Kumulative frekvenser
cum_laban <- freq_laban %>%
mutate(Kumulativ_frekvens = cumsum(n))
cum_coop <- freq_coop %>%
mutate(Kumulativ_frekvens = cumsum(n))
cum_laban
cum_coop
#Medianer
mid_laban <- sum(cum_laban$Lengde*cum_laban$n) / sum(cum_laban$n)
mid_laban
mid_coop <- sum(cum_coop$Lengde*cum_coop$n) / sum(cum_coop$n)
mid_coop
med_pos_laban <- sum(cum_laban$n + 1) / 2
med_pos_laban
med_laban <- cum_laban$Lengde[which(cumsum(cum_laban$n) >= med_pos_laban)[1]]
med_pos_coop <- sum(cum_coop$n + 1) /2
med_pos_coop
med_coop <- cum_coop$Lengde[which(cumsum(cum_coop$n) >= med_pos_coop)[1]]
med_coop
med_laban
#Typetall
type_laban <- freq_laban$Lengde[which.max(freq_laban$n)]
type_coop <- freq_coop$Lengde[which.max(freq_coop$n)]
type_laban
type_coop
#Standardavvik
sd_laban <- sd(laban$Lengde)
sd_coop <- sd(coop$Lengde)
sd_laban
sd_coop
#Kumulative frekvensdiagrammer
cum_diag_laban <- ggplot(cum_laban, aes(x=`Lengde`, y=Kumulativ_frekvens)) +
geom_step(linewidth=0.9) +
geom_vline(aes(xintercept=mid_laban, color="Middelverdi"), linewidth=0.9) +
geom_vline(aes(xintercept=med_laban, color="Median"), linewidth=0.9) +
geom_vline(aes(xintercept=type_laban, color="Typetall (x_max)"), linewidth=0.9) +
geom_vline(aes(xintercept=mid_laban - sd_laban, color="middel − s"), linewidth=0.9,
linetype="dashed") +
geom_vline(aes(xintercept=mid_laban + sd_laban, color="middel + s"), linewidth=0.9,
linetype="dashed") +
labs(title="Kumulativt frekvensdiagram - Laban", x="Lengde", y="Kumulativ frekvens",
color="Linjer") +
theme_minimal() + theme(legend.position="bottom")
cum_diag_coop <- ggplot(cum_coop, aes(x=`Lengde`, y=Kumulativ_frekvens)) +
geom_step(linewidth=0.9) +
geom_vline(aes(xintercept=mid_coop, color="Middelverdi"), linewidth=0.9) +
geom_vline(aes(xintercept=med_coop, color="Median"), linewidth=0.9) +
geom_vline(aes(xintercept=type_coop, color="Typetall (x_max)"), linewidth=0.9) +
geom_vline(aes(xintercept=mid_coop - sd_coop, color="middel − s"), linewidth=0.9,
linetype="dashed") +
geom_vline(aes(xintercept=mid_coop + sd_coop, color="middel + s"), linewidth=0.9,
linetype="dashed") +
labs(title="Kumulativt frekvensdiagram - Coop", x="Lengde", y="Kumulativ frekvens",
color="Linjer") +
theme_minimal() + theme(legend.position="bottom")
cum_diag_laban
cum_diag_coop
#Frekvens diagram -
freq_diag_laban <- ggplot(freq_laban, aes(x=`Lengde`, y=n)) +
geom_col() +
geom_vline(aes(xintercept=mid_laban, color="Middelverdi"), linewidth=0.9) +
geom_vline(aes(xintercept=med_laban, color="Median"), linewidth=0.9) +
geom_vline(aes(xintercept=type_laban, color="Typetall (x_max)"), linewidth=0.9) +
geom_vline(aes(xintercept=mid_laban - sd_laban, color="x − s"), linewidth=0.9,
linetype="dashed") +
geom_vline(aes(xintercept=mid_laban + sd_laban, color="x + s"), linewidth=0.9,
linetype="dashed") +
labs(title="Frekvensdiagram - Laban", x="Lengde", y="Antall", color="Linjer") +
theme_minimal() + theme(legend.position="bottom")
freq_diag_coop <- ggplot(freq_coop, aes(x=`Lengde`, y=n)) +
geom_col() +
geom_vline(aes(xintercept=mid_coop, color="Middelverdi"), linewidth=0.9) +
geom_vline(aes(xintercept=med_coop, color="Median"), linewidth=0.9) +
geom_vline(aes(xintercept=type_coop, color="Typetall (x_max)"), linewidth=0.9) +
geom_vline(aes(xintercept=mid_coop - sd_coop, color="x − s"), linewidth=0.9,
linetype="dashed") +
geom_vline(aes(xintercept=mid_coop + sd_coop, color="x + s"), linewidth=0.9,
linetype="dashed") +
labs(title="Frekvensdiagram - Coop", x="Lengde", y="Antall", color="Linjer") +
theme_minimal() + theme(legend.position="bottom")
freq_diag_laban
freq_diag_coop
#Oppsummering
tabell_laban <- data.frame(Mål = c("Middelverdi", "Median", "Typetall", "Standardavvik"),
Verdi = c(mid_laban, med_laban, type_laban, sd_laban))
tabell_coop <- data.frame(Mål = c("Middelverdi", "Median", "Typetall", "Standardavvik"),
Verdi = c(mid_coop, med_coop, type_coop, sd_coop))
tabell_laban
tabell_coop
oppsummering <- data.frame(Mål = c("Middelverdi", "Median", "Typetall", "Standardavvik"),
Laban = c(mid_laban, med_laban, type_laban, sd_laban),
Coop = c(mid_coop, med_coop, type_coop, sd_coop))
oppsummering$Laban <- round(oppsummering$Laban, 2)
oppsummering$Coop <- round(oppsummering$Coop, 2)
oppsummering
write.csv(oppsummering, "oppsummering.csv", row.names = FALSE, quote = FALSE)

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Mål,Laban,Coop
Middelverdi,8.09,11.52
Median,8,12
Typetall,7,12
Standardavvik,0.97,1.34
1 Mål Laban Coop
2 Middelverdi 8.09 11.52
3 Median 8 12
4 Typetall 7 12
5 Standardavvik 0.97 1.34

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Version: 1.0
RestoreWorkspace: Default
SaveWorkspace: Default
AlwaysSaveHistory: Default
EnableCodeIndexing: Yes
UseSpacesForTab: Yes
NumSpacesForTab: 2
Encoding: UTF-8
RnwWeave: Sweave
LaTeX: pdfLaTeX

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#Hvor mange måter kan du plukke 5 elementer fra 12
#når trekket er...
n <- 12
k <- 5
#a) ordnet, med tilbakelegging
n^k
#b) uordnet, med tilbakelegging
choose((n + k - 1), k)
#c) ordnet, uten tilbakelegging
factorial(n) / factorial(n - k)
#d) uordnet, uten tilbakelegging
choose(n, k)
#Eksempel på a) - PIN-kode med 5 siffer. Man kan gjenbruke ett siffer flere
#ganger
#Eksempel på b) - Velg 5 is-kuler fra et utvalg av 5 smaker. Hver kule trenger
#ikke være unik
#Eksempel på c) - Velg 5 studenter fra en gruppe på 12 og sorter dem etter alder
#Eksempel på d) - Trekk 5 kort fra en bunke på 12 uten å legge dem tilbake

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#Twist-posen
#a) Du skal rydde opp etter en fest, og finner en Twist-pose med kun 7 kokos
#og 13 lakris igjen. Du plukker en tilfeldig twist. Hva er sannsynligheten
#for at den blir en kokos?
kokos <- 7
lakris <- 13
total = kokos + lakris
P_kokos = kokos / total
#b) Du liker verken lakris eller kokos, så du legger den du har plukket tilbake
#i posen for å plukke en ny. Du prøver deg slik 5 ganger, og legger tilbake
#for hver gang. Lag stoplediagram over sannsynligheten for at du har plukket
#kokos respektivt 0, 1, 2, 3, 4 og 5 ganger
N <- total
S <- kokos
p <- S / N
n <- 5
#Formel 4.2.3 i formelheftet
ProbComb = function(k){
choose(n, k) * (p^k) * (1 - p)^(n - k)
}
ProbComb(0)
ProbComb(1)
ProbComb(2)
ProbComb(3)
ProbComb(4)
ProbComb(5)
#Litt senere på morran er du så sultern at selv kokos og lakris går an, så
#du plukker 5 twist og spiser dem. Lag stolpediagram over sannsynligheten for
#at du spiser respektive 0, 1, 2, 3, 4 og 5 kokos
ProbCombNoReplace = function(k){
(choose(S, k) * choose((N - S), n - k) / choose(N, n))
}
ProbCombNoReplace(0)
ProbCombNoReplace(1)
ProbCombNoReplace(2)
ProbCombNoReplace(3)
ProbCombNoReplace(4)
ProbCombNoReplace(5)
#Diagrammer
k_values <- 0:n
probs_binom <- sapply(k_values, ProbComb)
probs_hyper <- sapply(k_values, ProbCombNoReplace)
max_b <- max(probs_binom)
max_h <- max(probs_hyper)
max_y <- max(max_b, max_h)
ylim_val <- c(0, max_y * 1.1)
par(mfrow = c(1, 2))
barplot(probs_binom, names.arg = k_values, col = "steelblue",
ylim = ylim_val, xlab = "Antall kokos", ylab = "Sannsynlighet",
main = "Med tilbakelegging")
barplot(probs_hyper, names.arg = k_values, col = "darkorange",
ylim = ylim_val, xlab = "Antall kokos", ylab = "Sannsynlighet",
main = "Uten tilbakelegging")
par(mfrow = c(1, 1))

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install.packages("VennDiagram")
library(VennDiagram)
P_A <- 0.8
P_B <- 0.2
P_AB <- 0.1
bare_A <- P_A - P_AB
bare_B <- P_B - P_AB
utenfor <- 1 - (bare_A + bare_B + P_AB)
bare_A
bare_B
utenfor
#Sjekk at verdier stemmer
bare_A + bare_B + utenfor + P_AB
#3b
P_union <- P_A + P_B - P_AB
P_union
P_A_uten_B <- bare_A
P_A_uten_B
#3c
P_komplement_intersection <- 1 - P_AB
P_komplement_intersection
#DeMorgan's lov sier at P(AB)^c = P(A^c u B^c)
#Derfor er sannsynligheten den samme
#3d
P_A_gitt_B <- P_AB / P_B
P_B_gitt_A <- P_AB / P_A
P_A_gitt_B
P_B_gitt_A
#Forskjellen mellom disse to er at P_A_gitt_B er
#sannsynligheten for at A skjer gitt at B allerede
#har skjedd - P_B_gitt_A er da sannsynligheten for
#at B skjer gitt at A allerede har skjedd
#Venn Diagrammet
draw.pairwise.venn(area1 = P_A, area2 = P_B,
cross.area = P_AB, category = c("A", "B"),
fill = c("lightblue", "pink"),
lty = "blank")

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#4a
myChoose = function(n, k){
factorial(n) / (factorial(k) * factorial(n - k))
}
choose(4, 2)
myChoose(4, 2)
#4b
#Definerer funksjonen bd med parameter n
bd = function(n){
#Setter antall "frie" dager
dager = 365 + 1 - 1:n
#Deler antall "frie" dager på antall
#dager i et år - gir et desimaltall som
#ganges med 100 for å få den eksakte prosentverdien
#for sannsynligheten at ingen i samme set har
#samme bursdag
sjanser = dager / 365
#Utfører utregningen og lagrer resultatet til
#variablen output
output = prod(sjanser)
#Printer resultatet
output
}
#Regner ut og printer sannsynligheten for at
#to personer i samme set har samme bursdag
#Vi gjør "1 - bd()" for å finne sannsynligheten
1 - bd(22)
1 - bd(23)
#Denne funksjonen regner sannsynligheten for at ingen
#personer i samme set har bursdag på samme dag
#Bursdagsparadokset er et berømt statistikk eksempel
#4c
#Setter startpunktet til en Random Number Generator(RNG)
set.seed(314)
#Lager en mengde / sekvens fra 3 til 27 (3, 4, 5, ..., 27)
base = 3:27
#Trekker 14 tall fra sekvensen "base" med tilbakelegging
a = sample(base, 14, replace=TRUE)
#4d
totalSum = 0
for(verdi in a){
totalSum = totalSum + verdi
}
totalSum
sum(a)
#4e
totalProd = 1
for (verdi in a) {
totalProd = totalProd * verdi
}
totalProd
prod(a)
#4f
#Med tilbakelegging - kan få samme verdi flere gange
a = sample(base, 14, replace=TRUE)
sort(a)
#Uten tilbakelegging - kan kun få atomære verdier
a = sample(base, 14, replace=FALSE)
sort(a)

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EnableCodeIndexing: Yes
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# ============================================================
# Oppgave 3g -- Symmetrisk 90% intervallestimat
# Genererer pdf, CDF og iCDF for alle 8 grupper
# med markerte 5. og 95. prosentiler
# ============================================================
install.packages(c("ggplot2", "patchwork", "scales"))
library(ggplot2)
library(patchwork)
col_curve <- "red3"
col_shade <- scales::alpha("red3", 0.2)
col_mark <- "steelblue"
theme_oblig <- theme_classic() +
theme(
axis.title = element_text(size = 9),
axis.text = element_text(size = 8),
plot.title = element_text(size = 10, face = "bold")
)
# Hjelpefunksjon for segmenter (unngaar advarsler fra geom_segment med aes)
seg <- function(x1, y1, x2, y2, ...) {
annotate("segment", x = x1, xend = x2, y = y1, yend = y2, ...)
}
# Lagringsfunksjon med feilhåndtering
lagre_gruppe <- function(navn, pdf_plot, cdf_plot, icdf_plot) {
tryCatch({
kombinert <- pdf_plot + cdf_plot + icdf_plot +
plot_annotation(
title = paste("Gruppe", navn),
theme = theme(plot.title = element_text(size = 12, face = "bold"))
)
ggsave(paste0("gruppe_", navn, ".png"), kombinert,
width = 12, height = 4, dpi = 150)
message("OK: gruppe_", navn, ".png lagret")
}, error = function(e) {
message("FEIL gruppe ", navn, ": ", conditionMessage(e))
})
}
# x-vektor for kontinuerlige fordelinger (brukes av d, e, f, g, h)
x_kont <- seq(0, 10, length.out = 500)
# ============================================================
# GRUPPE a -- Diskret, ujevn
# ============================================================
tryCatch({
vals_a <- 1:10
prob_a <- c(0.03, 0.08, 0.09, 0.03, 0.03, 0.065, 0.14, 0.21, 0.19, 0.075)
prob_a <- prob_a / sum(prob_a)
cdf_a <- cumsum(prob_a)
p05_a <- min(vals_a[cdf_a >= 0.05])
p95_a <- min(vals_a[cdf_a >= 0.95])
df_a <- data.frame(x = vals_a, f = prob_a, F = cdf_a)
pdf_a <- ggplot(df_a, aes(x, f)) +
geom_bar(stat = "identity",
fill = ifelse(vals_a >= p05_a & vals_a <= p95_a, col_shade, "white"),
color = col_curve, width = 0.4) +
geom_vline(xintercept = c(p05_a, p95_a), color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_a, y = max(prob_a) * 0.95,
label = paste0("x[0.05]==", p05_a), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_a, y = max(prob_a) * 0.95,
label = paste0("x[0.95]==", p95_a), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
scale_x_continuous(breaks = 1:10) +
labs(title = "pdf a", x = "x", y = "f(x)") + theme_oblig
cdf_a_plot <- ggplot(df_a, aes(x, F)) +
geom_step(color = col_curve, linewidth = 0.8) +
geom_point(color = col_curve, size = 2) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_a, 0, p05_a, 0.05, color = col_mark, linewidth = 0.8) +
seg(p95_a, 0, p95_a, 0.95, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_a, y = 0.08,
label = paste0("x[0.05]==", p05_a), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_a, y = 0.92,
label = paste0("x[0.95]==", p95_a), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
scale_x_continuous(breaks = 1:10) +
labs(title = "CDF E", x = "x", y = "F(x)") + theme_oblig
icdf_a_df <- data.frame(p = c(0, cdf_a), x = c(vals_a[1], vals_a))
icdf_a_plot <- ggplot(icdf_a_df, aes(p, x)) +
geom_step(color = col_curve, linewidth = 0.8, direction = "vh") +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
scale_y_continuous(breaks = 1:10) +
labs(title = "iCDF (a)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("a", pdf_a, cdf_a_plot, icdf_a_plot)
}, error = function(e) message("FEIL gruppe a: ", e$message))
# ============================================================
# GRUPPE b -- Diskret, synkende
# ============================================================
tryCatch({
vals_b <- 1:10
prob_b <- c(0.40, 0.25, 0.13, 0.08, 0.05, 0.04, 0.02, 0.015, 0.01, 0.005)
prob_b <- prob_b / sum(prob_b)
cdf_b <- cumsum(prob_b)
p05_b <- min(vals_b[cdf_b >= 0.05])
p95_b <- min(vals_b[cdf_b >= 0.95])
df_b <- data.frame(x = vals_b, f = prob_b, F = cdf_b)
pdf_b <- ggplot(df_b, aes(x, f)) +
geom_bar(stat = "identity",
fill = ifelse(vals_b >= p05_b & vals_b <= p95_b, col_shade, "white"),
color = col_curve, width = 0.4) +
geom_vline(xintercept = c(p05_b, p95_b), color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_b, y = max(prob_b) * 0.95,
label = paste0("x[0.05]==", p05_b), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_b, y = max(prob_b) * 0.70,
label = paste0("x[0.95]==", p95_b), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
scale_x_continuous(breaks = 1:10) +
labs(title = "pdf b", x = "x", y = "f(x)") + theme_oblig
cdf_b_plot <- ggplot(df_b, aes(x, F)) +
geom_step(color = col_curve, linewidth = 0.8) +
geom_point(color = col_curve, size = 2) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_b, 0, p05_b, 0.05, color = col_mark, linewidth = 0.8) +
seg(p95_b, 0, p95_b, 0.95, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_b, y = 0.08,
label = paste0("x[0.05]==", p05_b), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_b, y = 0.92,
label = paste0("x[0.95]==", p95_b), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
scale_x_continuous(breaks = 1:10) +
labs(title = "CDF C", x = "x", y = "F(x)") + theme_oblig
icdf_b_df <- data.frame(p = c(0, cdf_b), x = c(vals_b[1], vals_b))
icdf_b_plot <- ggplot(icdf_b_df, aes(p, x)) +
geom_step(color = col_curve, linewidth = 0.8, direction = "vh") +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
scale_y_continuous(breaks = 1:10) +
labs(title = "iCDF (b)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("b", pdf_b, cdf_b_plot, icdf_b_plot)
}, error = function(e) message("FEIL gruppe b: ", e$message))
# ============================================================
# GRUPPE c -- Diskret, uniform
# ============================================================
tryCatch({
vals_c <- 1:10
prob_c <- rep(0.1, 10)
cdf_c <- cumsum(prob_c)
p05_c <- min(vals_c[cdf_c >= 0.05])
p95_c <- min(vals_c[cdf_c >= 0.95])
df_c <- data.frame(x = vals_c, f = prob_c, F = cdf_c)
pdf_c <- ggplot(df_c, aes(x, f)) +
geom_bar(stat = "identity", fill = col_shade, color = col_curve, width = 0.4) +
geom_vline(xintercept = c(p05_c, p95_c), color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_c, y = 0.13,
label = paste0("x[0.05]==", p05_c), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_c, y = 0.13,
label = paste0("x[0.95]==", p95_c), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
scale_x_continuous(breaks = 1:10) + ylim(0, 0.15) +
labs(title = "pdf c", x = "x", y = "f(x)") + theme_oblig
cdf_c_plot <- ggplot(df_c, aes(x, F)) +
geom_step(color = col_curve, linewidth = 0.8) +
geom_point(color = col_curve, size = 2) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_c, 0, p05_c, 0.05, color = col_mark, linewidth = 0.8) +
seg(p95_c, 0, p95_c, 0.95, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_c, y = 0.08,
label = paste0("x[0.05]==", p05_c), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_c, y = 0.92,
label = paste0("x[0.95]==", p95_c), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
scale_x_continuous(breaks = 1:10) +
labs(title = "CDF G", x = "x", y = "F(x)") + theme_oblig
icdf_c_df <- data.frame(p = c(0, cdf_c), x = c(vals_c[1], vals_c))
icdf_c_plot <- ggplot(icdf_c_df, aes(p, x)) +
geom_step(color = col_curve, linewidth = 0.8, direction = "vh") +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
scale_y_continuous(breaks = 1:10) +
labs(title = "iCDF (c)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("c", pdf_c, cdf_c_plot, icdf_c_plot)
}, error = function(e) message("FEIL gruppe c: ", e$message))
# ============================================================
# GRUPPE d -- Kontinuerlig, bimodal
# ============================================================
tryCatch({
pdf_d_fun <- function(x) 0.55 * dnorm(x, 2, 0.9) + 0.45 * dnorm(x, 6, 1.2)
cdf_d_fun <- function(x) 0.55 * pnorm(x, 2, 0.9) + 0.45 * pnorm(x, 6, 1.2)
p05_d <- uniroot(function(x) cdf_d_fun(x) - 0.05, c(-5, 15))$root
p95_d <- uniroot(function(x) cdf_d_fun(x) - 0.95, c(-5, 15))$root
df_d <- data.frame(x = x_kont, f = pdf_d_fun(x_kont), F = cdf_d_fun(x_kont))
# iCDF via approxfun (unngaar uniroot-feil)
x_vid <- seq(-3, 13, length.out = 3000)
icdf_d_fn <- approxfun(cdf_d_fun(x_vid), x_vid, rule = 2)
p_seq_d <- seq(0.001, 0.999, length.out = 400)
df_icdf_d <- data.frame(p = p_seq_d, x = icdf_d_fn(p_seq_d))
pdf_d <- ggplot(df_d, aes(x, f)) +
geom_area(data = subset(df_d, x >= p05_d & x <= p95_d), fill = col_shade) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(p05_d, p95_d), color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_d, y = max(df_d$f) * 0.95,
label = sprintf("x[0.05]==%.2f", p05_d), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_d, y = max(df_d$f) * 0.95,
label = sprintf("x[0.95]==%.2f", p95_d), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
labs(title = "pdf d", x = "x", y = "f(x)") + theme_oblig
cdf_d_plot <- ggplot(df_d, aes(x, F)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_d, 0, p05_d, 0.05, color = col_mark, linewidth = 0.8) +
seg(p95_d, 0, p95_d, 0.95, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_d, y = 0.08,
label = sprintf("%.2f", p05_d), hjust = -0.2, size = 3, color = col_mark) +
annotate("text", x = p95_d, y = 0.92,
label = sprintf("%.2f", p95_d), hjust = 1.2, size = 3, color = col_mark) +
labs(title = "CDF A", x = "x", y = "F(x)") + theme_oblig
icdf_d_plot <- ggplot(df_icdf_d, aes(p, x)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(0.05, 0, 0.05, p05_d, color = col_mark, linewidth = 0.8) +
seg(0.95, 0, 0.95, p95_d, color = col_mark, linewidth = 0.8) +
annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
labs(title = "iCDF (d)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("d", pdf_d, cdf_d_plot, icdf_d_plot)
}, error = function(e) message("FEIL gruppe d: ", e$message))
# ============================================================
# GRUPPE e -- Normal(5, 1.5)
# ============================================================
tryCatch({
mu_e <- 5; sigma_e <- 1.5
p05_e <- qnorm(0.05, mu_e, sigma_e)
p95_e <- qnorm(0.95, mu_e, sigma_e)
df_e <- data.frame(x = x_kont,
f = dnorm(x_kont, mu_e, sigma_e),
F = pnorm(x_kont, mu_e, sigma_e))
p_seq_e <- seq(0.001, 0.999, length.out = 300)
df_icdf_e <- data.frame(p = p_seq_e, x = qnorm(p_seq_e, mu_e, sigma_e))
pdf_e <- ggplot(df_e, aes(x, f)) +
geom_area(data = subset(df_e, x >= p05_e & x <= p95_e), fill = col_shade) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(p05_e, p95_e), color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_e, y = max(df_e$f) * 0.95,
label = sprintf("x[0.05]==%.2f", p05_e), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_e, y = max(df_e$f) * 0.95,
label = sprintf("x[0.95]==%.2f", p95_e), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
labs(title = "pdf e", x = "x", y = "f(x)") + theme_oblig
cdf_e_plot <- ggplot(df_e, aes(x, F)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_e, 0, p05_e, 0.05, color = col_mark, linewidth = 0.8) +
seg(p95_e, 0, p95_e, 0.95, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_e, y = 0.08,
label = sprintf("%.2f", p05_e), hjust = -0.2, size = 3, color = col_mark) +
annotate("text", x = p95_e, y = 0.92,
label = sprintf("%.2f", p95_e), hjust = 1.2, size = 3, color = col_mark) +
labs(title = "CDF H", x = "x", y = "F(x)") + theme_oblig
icdf_e_plot <- ggplot(df_icdf_e, aes(p, x)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(0.05, 0, 0.05, p05_e, color = col_mark, linewidth = 0.8) +
seg(0.95, 0, 0.95, p95_e, color = col_mark, linewidth = 0.8) +
annotate("text", x = 0.05, y = 9,
label = sprintf("%.2f", p05_e), hjust = -0.2, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = 9,
label = sprintf("%.2f", p95_e), hjust = 1.2, size = 3, color = col_mark) +
labs(title = "iCDF (e)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("e", pdf_e, cdf_e_plot, icdf_e_plot)
}, error = function(e) message("FEIL gruppe e: ", e$message))
# ============================================================
# GRUPPE f -- Uniform(0, 10)
# ============================================================
tryCatch({
p05_f <- qunif(0.05, 0, 10)
p95_f <- qunif(0.95, 0, 10)
df_f <- data.frame(x = x_kont,
f = dunif(x_kont, 0, 10),
F = punif(x_kont, 0, 10))
p_seq_f <- seq(0, 1, length.out = 300)
df_icdf_f <- data.frame(p = p_seq_f, x = qunif(p_seq_f, 0, 10))
pdf_f <- ggplot(df_f, aes(x, f)) +
geom_area(data = subset(df_f, x >= p05_f & x <= p95_f), fill = col_shade) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(p05_f, p95_f), color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_f, y = 0.13,
label = sprintf("x[0.05]==%.1f", p05_f), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_f, y = 0.13,
label = sprintf("x[0.95]==%.1f", p95_f), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
ylim(0, 0.15) +
labs(title = "pdf f", x = "x", y = "f(x)") + theme_oblig
cdf_f_plot <- ggplot(df_f, aes(x, F)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_f, 0, p05_f, 0.05, color = col_mark, linewidth = 0.8) +
seg(p95_f, 0, p95_f, 0.95, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_f, y = 0.08,
label = sprintf("%.1f", p05_f), hjust = -0.3, size = 3, color = col_mark) +
annotate("text", x = p95_f, y = 0.92,
label = sprintf("%.1f", p95_f), hjust = 1.3, size = 3, color = col_mark) +
labs(title = "CDF B", x = "x", y = "F(x)") + theme_oblig
icdf_f_plot <- ggplot(df_icdf_f, aes(p, x)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(0.05, 0, 0.05, p05_f, color = col_mark, linewidth = 0.8) +
seg(0.95, 0, 0.95, p95_f, color = col_mark, linewidth = 0.8) +
annotate("text", x = 0.05, y = 9,
label = sprintf("%.1f", p05_f), hjust = -0.3, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = 9,
label = sprintf("%.1f", p95_f), hjust = 1.3, size = 3, color = col_mark) +
labs(title = "iCDF (f)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("f", pdf_f, cdf_f_plot, icdf_f_plot)
}, error = function(e) message("FEIL gruppe f: ", e$message))
# ============================================================
# GRUPPE g -- Triangel(0, 10). F(x) = x^2/100
# ============================================================
tryCatch({
p05_g <- 10 * sqrt(0.05)
p95_g <- 10 * sqrt(0.95)
pdf_g_f <- function(x) ifelse(x >= 0 & x <= 10, x / 50, 0)
cdf_g_f <- function(x) ifelse(x < 0, 0, ifelse(x > 10, 1, x^2 / 100))
df_g <- data.frame(x = x_kont, f = pdf_g_f(x_kont), F = cdf_g_f(x_kont))
p_seq_g <- seq(0, 1, length.out = 300)
df_icdf_g <- data.frame(p = p_seq_g, x = 10 * sqrt(p_seq_g))
pdf_g <- ggplot(df_g, aes(x, f)) +
geom_area(data = subset(df_g, x >= p05_g & x <= p95_g), fill = col_shade) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(p05_g, p95_g), color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_g, y = 0.23,
label = sprintf("x[0.05]==%.2f", p05_g), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = p95_g, y = 0.23,
label = sprintf("x[0.95]==%.2f", p95_g), parse = TRUE,
hjust = 1.1, size = 3, color = col_mark) +
labs(title = "pdf g", x = "x", y = "f(x)") + theme_oblig
cdf_g_plot <- ggplot(df_g, aes(x, F)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_g, 0, p05_g, 0.05, color = col_mark, linewidth = 0.8) +
seg(p95_g, 0, p95_g, 0.95, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_g, y = 0.08,
label = sprintf("%.2f", p05_g), hjust = -0.2, size = 3, color = col_mark) +
annotate("text", x = p95_g, y = 0.92,
label = sprintf("%.2f", p95_g), hjust = 1.2, size = 3, color = col_mark) +
labs(title = "CDF F", x = "x", y = "F(x)") + theme_oblig
icdf_g_plot <- ggplot(df_icdf_g, aes(p, x)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(0.05, 0, 0.05, p05_g, color = col_mark, linewidth = 0.8) +
seg(0.95, 0, 0.95, p95_g, color = col_mark, linewidth = 0.8) +
annotate("text", x = 0.05, y = 9.5,
label = sprintf("%.2f", p05_g), hjust = -0.2, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = 9.5,
label = sprintf("%.2f", p95_g), hjust = 1.2, size = 3, color = col_mark) +
labs(title = "iCDF (g)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("g", pdf_g, cdf_g_plot, icdf_g_plot)
}, error = function(e) message("FEIL gruppe g: ", e$message))
# ============================================================
# GRUPPE h -- Eksponensiell(rate=0.2)
# 95. prosentil er ~15, utenfor x-aksen [0,10]
# ============================================================
tryCatch({
rate_h <- 0.2
p05_h <- qexp(0.05, rate_h)
p95_h <- qexp(0.95, rate_h)
df_h <- data.frame(x = x_kont,
f = dexp(x_kont, rate_h),
F = pexp(x_kont, rate_h))
p_seq_h <- seq(0.001, 0.99, length.out = 300)
df_icdf_h <- data.frame(p = p_seq_h, x = qexp(p_seq_h, rate_h))
pdf_h <- ggplot(df_h, aes(x, f)) +
geom_area(data = subset(df_h, x >= p05_h), fill = col_shade) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = p05_h, color = col_mark,
linetype = "dashed", linewidth = 0.8) +
annotate("text", x = p05_h, y = max(df_h$f) * 0.9,
label = sprintf("x[0.05]==%.2f", p05_h), parse = TRUE,
hjust = -0.1, size = 3, color = col_mark) +
annotate("text", x = 4.5, y = max(df_h$f) * 0.45,
label = "x[0.95] == 14.98 (utenfor)", parse = FALSE,
hjust = 0, size = 3, color = col_mark) +
labs(title = "pdf h", x = "x", y = "f(x)") + theme_oblig
cdf_h_plot <- ggplot(df_h, aes(x, F)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(p05_h, 0, p05_h, 0.05, color = col_mark, linewidth = 0.8) +
annotate("text", x = p05_h, y = 0.08,
label = sprintf("%.2f", p05_h), hjust = -0.2, size = 3, color = col_mark) +
annotate("text", x = 4, y = 0.95,
label = "x[0.95] = 14.98 (utenfor)", parse = FALSE,
hjust = 0, size = 3, color = col_mark) +
labs(title = "CDF D", x = "x", y = "F(x)") + theme_oblig
icdf_h_plot <- ggplot(df_icdf_h, aes(p, x)) +
geom_line(color = col_curve, linewidth = 0.8) +
geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
seg(0.05, 0, 0.05, p05_h, color = col_mark, linewidth = 0.8) +
seg(0.95, 0, 0.95, p95_h, color = col_mark, linewidth = 0.8) +
annotate("text", x = 0.05, y = max(df_icdf_h$x) * 0.9,
label = sprintf("%.2f", p05_h), hjust = -0.2, size = 3, color = col_mark) +
annotate("text", x = 0.95, y = max(df_icdf_h$x) * 0.9,
label = sprintf("%.2f", p95_h), hjust = 1.2, size = 3, color = col_mark) +
labs(title = "iCDF (h)", x = "p", y = "F-inv(p)") + theme_oblig
lagre_gruppe("h", pdf_h, cdf_h_plot, icdf_h_plot)
}, error = function(e) message("FEIL gruppe h: ", e$message))
message("\nFerdig! Sjekk konsollen for eventuelle feilmeldinger.")