5  Import i eksport danych. Wykresy. Zmienne losowe

Martyna Kosińska

5.1 📘 Eksport danych

# Uwaga. Przy eksporcie i później imporcie danych należy dostosować ścieżki dostępu 
# do plików do własnego komputera.

dane=head(swiss)    #Dane do eksportu.
dane
             Fertility Agriculture Examination Education Catholic
Courtelary        80.2        17.0          15        12     9.96
Delemont          83.1        45.1           6         9    84.84
Franches-Mnt      92.5        39.7           5         5    93.40
Moutier           85.8        36.5          12         7    33.77
Neuveville        76.9        43.5          17        15     5.16
Porrentruy        76.1        35.3           9         7    90.57
             Infant.Mortality
Courtelary               22.2
Delemont                 22.2
Franches-Mnt             20.2
Moutier                  20.3
Neuveville               20.6
Porrentruy               26.6

5.1.1 Eksport do pliku txt

write.table(dane,file="swiss_dane.txt",quote=F, row.names=T,col.names=T,sep="\t")

# Dla zapisania pliku w ustonym katalogu przykładowa komenda może być następująca:
# write.table(dane,file="C:/Users/Ania/Desktop/swiss_dane.txt",quote=F,row.names=T,col.names=T,sep="\t")

5.1.2 Eksport do pliku w formacie csv

write.csv(dane,"swiss_dane2.csv")
write.csv2(dane,"swiss_dane3.csv")

5.2 📘 Import danych

5.2.1 Import danych z pliku txt

im1=read.table("swiss_dane.txt",header=T,sep="\t")
# Dla odczytu pliku a ustalonego katalogu przykładowa komenda może być następująca:
# im1=read.table("C:/Users/Ania/Desktop/swiss_dane.txt",header=T,sep="\t")
im1
             Fertility Agriculture Examination Education Catholic
Courtelary        80.2        17.0          15        12     9.96
Delemont          83.1        45.1           6         9    84.84
Franches-Mnt      92.5        39.7           5         5    93.40
Moutier           85.8        36.5          12         7    33.77
Neuveville        76.9        43.5          17        15     5.16
Porrentruy        76.1        35.3           9         7    90.57
             Infant.Mortality
Courtelary               22.2
Delemont                 22.2
Franches-Mnt             20.2
Moutier                  20.3
Neuveville               20.6
Porrentruy               26.6

5.2.2 Import danych z pliku csv (separatorem dziesiętnym jest ,)

im2=read.csv2("swiss_dane3.csv")
head(im2)
             X Fertility Agriculture Examination Education Catholic
1   Courtelary      80.2        17.0          15        12     9.96
2     Delemont      83.1        45.1           6         9    84.84
3 Franches-Mnt      92.5        39.7           5         5    93.40
4      Moutier      85.8        36.5          12         7    33.77
5   Neuveville      76.9        43.5          17        15     5.16
6   Porrentruy      76.1        35.3           9         7    90.57
  Infant.Mortality
1             22.2
2             22.2
3             20.2
4             20.3
5             20.6
6             26.6

5.2.3 Import danych z pliku csv (separatorem dziesiętnym jest .)

im3=read.csv("swiss_dane2.csv")
head(im3)
             X Fertility Agriculture Examination Education Catholic
1   Courtelary      80.2        17.0          15        12     9.96
2     Delemont      83.1        45.1           6         9    84.84
3 Franches-Mnt      92.5        39.7           5         5    93.40
4      Moutier      85.8        36.5          12         7    33.77
5   Neuveville      76.9        43.5          17        15     5.16
6   Porrentruy      76.1        35.3           9         7    90.57
  Infant.Mortality
1             22.2
2             22.2
3             20.2
4             20.3
5             20.6
6             26.6

5.2.4 Wklejanie ze schowka

# Import danych za pomocą wklejenia danych ze schowka. 
# Na początku pisze się kod, a następnie kopiuje dane, a potem wykonuje kod. 
# Dane można skopiować również na początku.
im4=read.delim2("clipboard",header=T)
im4
  cena wartość ilość
1 5.64  231.30  41.0
2 5.94  246.93  41.6
3 5.79  237.34  41.0
4 5.49  225.09  41.0
5 5.58  223.26  40.0
6 5.68  227.20  40.0
7 5.09  193.42  38.0
8 5.16  206.40  40.0

5.3 📘 Katalog roboczy

#Sprawdzenie jaki jest katalog roboczy - gdzie się znajduje.

getwd()
[1] "E:/Doc_UE/Quatro/Samouczek"
# Zmiana katalogu roboczego.
# Zamieniamy obecny katalog roboczy, żeby pracować w innym katalogu i nie musieć podawać ścieżki dostępu do plików przy imporcie czy eksporcie danych.

setwd("C:/Users/Ania/Desktop")
Error in setwd("C:/Users/Ania/Desktop"): nie można zmienić katalogu roboczego
getwd() #Faktycznie katalog roboczy został zmieniony.
[1] "E:/Doc_UE/Quatro/Samouczek"
# Eksport pliku do folderu o domyślnej lokalizacji. 
write.csv2(dane,"iris1.csv")  #Nie podaje się już ścieżki dostępu, tylko jak ma się nazywać plik zz danymi i jego rozszerzenie (w cudzysłowie). 

# Import pliku z folderu o domyślnej lokalizacji.
read.csv2("iris1.csv")  #Nie podaje się już ścieżki dostępu do pliku, tylko w cudzysłowie zamieszcza się nazwę i rozszerzenie pliku, który chcesię  zaimportować do R.
             X Fertility Agriculture Examination Education Catholic
1   Courtelary      80.2        17.0          15        12     9.96
2     Delemont      83.1        45.1           6         9    84.84
3 Franches-Mnt      92.5        39.7           5         5    93.40
4      Moutier      85.8        36.5          12         7    33.77
5   Neuveville      76.9        43.5          17        15     5.16
6   Porrentruy      76.1        35.3           9         7    90.57
  Infant.Mortality
1             22.2
2             22.2
3             20.2
4             20.3
5             20.6
6             26.6

5.4 📘 Podstawowe wykresy

x=c(65,43,21,43,57)
y=c(0,0.5,3,2.2,5)

plot(x)

plot(x,type="l")

plot(x,type="p")

plot(x,type="b")

plot(x,type="h")

plot(x,type="s")

plot(x,type="l",col=6)

plot(x,type="l",col=6,lwd=3)

plot(x,type="l",col=6,lwd=3,lty=5)

plot(x,type="l",col=6,lwd=3,lty=2)

plot(x,y)

plot(x,y,lwd=2)

plot(x,y,lwd=2,main="Czas sprzątania względem wieku")

plot(x,y,lwd=2,main="Czas sprzątania względem wieku",xlab="wiek")

plot(x,y,lwd=2,main="Czas sprzątania względem wieku",xlab="wiek",ylab="czas sprzątania")

?AirPassengers
uruchamianie serwera httpd dla pomocy ... wykonano
plot(AirPassengers)

class(AirPassengers)
[1] "ts"

5.4.1 Histogram

trees
   Girth Height Volume
1    8.3     70   10.3
2    8.6     65   10.3
3    8.8     63   10.2
4   10.5     72   16.4
5   10.7     81   18.8
6   10.8     83   19.7
7   11.0     66   15.6
8   11.0     75   18.2
9   11.1     80   22.6
10  11.2     75   19.9
11  11.3     79   24.2
12  11.4     76   21.0
13  11.4     76   21.4
14  11.7     69   21.3
15  12.0     75   19.1
16  12.9     74   22.2
17  12.9     85   33.8
18  13.3     86   27.4
19  13.7     71   25.7
20  13.8     64   24.9
21  14.0     78   34.5
22  14.2     80   31.7
23  14.5     74   36.3
24  16.0     72   38.3
25  16.3     77   42.6
26  17.3     81   55.4
27  17.5     82   55.7
28  17.9     80   58.3
29  18.0     80   51.5
30  18.0     80   51.0
31  20.6     87   77.0
hist(trees$Height)

hist(trees$Height,prob=T)
hist(trees$Height,freq=F)

par(mfrow=c(2,1))
hist(trees$Height)
hist(trees$Height,prob=T)

par(mfrow=c(1,1))
hist(trees$Height)

hist(trees$Height,breaks=10)

hist(trees$Height,breaks=c(60,70,80,90,100))

hist(trees$Height,col="pink")

colors()
  [1] "white"                "aliceblue"            "antiquewhite"        
  [4] "antiquewhite1"        "antiquewhite2"        "antiquewhite3"       
  [7] "antiquewhite4"        "aquamarine"           "aquamarine1"         
 [10] "aquamarine2"          "aquamarine3"          "aquamarine4"         
 [13] "azure"                "azure1"               "azure2"              
 [16] "azure3"               "azure4"               "beige"               
 [19] "bisque"               "bisque1"              "bisque2"             
 [22] "bisque3"              "bisque4"              "black"               
 [25] "blanchedalmond"       "blue"                 "blue1"               
 [28] "blue2"                "blue3"                "blue4"               
 [31] "blueviolet"           "brown"                "brown1"              
 [34] "brown2"               "brown3"               "brown4"              
 [37] "burlywood"            "burlywood1"           "burlywood2"          
 [40] "burlywood3"           "burlywood4"           "cadetblue"           
 [43] "cadetblue1"           "cadetblue2"           "cadetblue3"          
 [46] "cadetblue4"           "chartreuse"           "chartreuse1"         
 [49] "chartreuse2"          "chartreuse3"          "chartreuse4"         
 [52] "chocolate"            "chocolate1"           "chocolate2"          
 [55] "chocolate3"           "chocolate4"           "coral"               
 [58] "coral1"               "coral2"               "coral3"              
 [61] "coral4"               "cornflowerblue"       "cornsilk"            
 [64] "cornsilk1"            "cornsilk2"            "cornsilk3"           
 [67] "cornsilk4"            "cyan"                 "cyan1"               
 [70] "cyan2"                "cyan3"                "cyan4"               
 [73] "darkblue"             "darkcyan"             "darkgoldenrod"       
 [76] "darkgoldenrod1"       "darkgoldenrod2"       "darkgoldenrod3"      
 [79] "darkgoldenrod4"       "darkgray"             "darkgreen"           
 [82] "darkgrey"             "darkkhaki"            "darkmagenta"         
 [85] "darkolivegreen"       "darkolivegreen1"      "darkolivegreen2"     
 [88] "darkolivegreen3"      "darkolivegreen4"      "darkorange"          
 [91] "darkorange1"          "darkorange2"          "darkorange3"         
 [94] "darkorange4"          "darkorchid"           "darkorchid1"         
 [97] "darkorchid2"          "darkorchid3"          "darkorchid4"         
[100] "darkred"              "darksalmon"           "darkseagreen"        
[103] "darkseagreen1"        "darkseagreen2"        "darkseagreen3"       
[106] "darkseagreen4"        "darkslateblue"        "darkslategray"       
[109] "darkslategray1"       "darkslategray2"       "darkslategray3"      
[112] "darkslategray4"       "darkslategrey"        "darkturquoise"       
[115] "darkviolet"           "deeppink"             "deeppink1"           
[118] "deeppink2"            "deeppink3"            "deeppink4"           
[121] "deepskyblue"          "deepskyblue1"         "deepskyblue2"        
[124] "deepskyblue3"         "deepskyblue4"         "dimgray"             
[127] "dimgrey"              "dodgerblue"           "dodgerblue1"         
[130] "dodgerblue2"          "dodgerblue3"          "dodgerblue4"         
[133] "firebrick"            "firebrick1"           "firebrick2"          
[136] "firebrick3"           "firebrick4"           "floralwhite"         
[139] "forestgreen"          "gainsboro"            "ghostwhite"          
[142] "gold"                 "gold1"                "gold2"               
[145] "gold3"                "gold4"                "goldenrod"           
[148] "goldenrod1"           "goldenrod2"           "goldenrod3"          
[151] "goldenrod4"           "gray"                 "gray0"               
[154] "gray1"                "gray2"                "gray3"               
[157] "gray4"                "gray5"                "gray6"               
[160] "gray7"                "gray8"                "gray9"               
[163] "gray10"               "gray11"               "gray12"              
[166] "gray13"               "gray14"               "gray15"              
[169] "gray16"               "gray17"               "gray18"              
[172] "gray19"               "gray20"               "gray21"              
[175] "gray22"               "gray23"               "gray24"              
[178] "gray25"               "gray26"               "gray27"              
[181] "gray28"               "gray29"               "gray30"              
[184] "gray31"               "gray32"               "gray33"              
[187] "gray34"               "gray35"               "gray36"              
[190] "gray37"               "gray38"               "gray39"              
[193] "gray40"               "gray41"               "gray42"              
[196] "gray43"               "gray44"               "gray45"              
[199] "gray46"               "gray47"               "gray48"              
[202] "gray49"               "gray50"               "gray51"              
[205] "gray52"               "gray53"               "gray54"              
[208] "gray55"               "gray56"               "gray57"              
[211] "gray58"               "gray59"               "gray60"              
[214] "gray61"               "gray62"               "gray63"              
[217] "gray64"               "gray65"               "gray66"              
[220] "gray67"               "gray68"               "gray69"              
[223] "gray70"               "gray71"               "gray72"              
[226] "gray73"               "gray74"               "gray75"              
[229] "gray76"               "gray77"               "gray78"              
[232] "gray79"               "gray80"               "gray81"              
[235] "gray82"               "gray83"               "gray84"              
[238] "gray85"               "gray86"               "gray87"              
[241] "gray88"               "gray89"               "gray90"              
[244] "gray91"               "gray92"               "gray93"              
[247] "gray94"               "gray95"               "gray96"              
[250] "gray97"               "gray98"               "gray99"              
[253] "gray100"              "green"                "green1"              
[256] "green2"               "green3"               "green4"              
[259] "greenyellow"          "grey"                 "grey0"               
[262] "grey1"                "grey2"                "grey3"               
[265] "grey4"                "grey5"                "grey6"               
[268] "grey7"                "grey8"                "grey9"               
[271] "grey10"               "grey11"               "grey12"              
[274] "grey13"               "grey14"               "grey15"              
[277] "grey16"               "grey17"               "grey18"              
[280] "grey19"               "grey20"               "grey21"              
[283] "grey22"               "grey23"               "grey24"              
[286] "grey25"               "grey26"               "grey27"              
[289] "grey28"               "grey29"               "grey30"              
[292] "grey31"               "grey32"               "grey33"              
[295] "grey34"               "grey35"               "grey36"              
[298] "grey37"               "grey38"               "grey39"              
[301] "grey40"               "grey41"               "grey42"              
[304] "grey43"               "grey44"               "grey45"              
[307] "grey46"               "grey47"               "grey48"              
[310] "grey49"               "grey50"               "grey51"              
[313] "grey52"               "grey53"               "grey54"              
[316] "grey55"               "grey56"               "grey57"              
[319] "grey58"               "grey59"               "grey60"              
[322] "grey61"               "grey62"               "grey63"              
[325] "grey64"               "grey65"               "grey66"              
[328] "grey67"               "grey68"               "grey69"              
[331] "grey70"               "grey71"               "grey72"              
[334] "grey73"               "grey74"               "grey75"              
[337] "grey76"               "grey77"               "grey78"              
[340] "grey79"               "grey80"               "grey81"              
[343] "grey82"               "grey83"               "grey84"              
[346] "grey85"               "grey86"               "grey87"              
[349] "grey88"               "grey89"               "grey90"              
[352] "grey91"               "grey92"               "grey93"              
[355] "grey94"               "grey95"               "grey96"              
[358] "grey97"               "grey98"               "grey99"              
[361] "grey100"              "honeydew"             "honeydew1"           
[364] "honeydew2"            "honeydew3"            "honeydew4"           
[367] "hotpink"              "hotpink1"             "hotpink2"            
[370] "hotpink3"             "hotpink4"             "indianred"           
[373] "indianred1"           "indianred2"           "indianred3"          
[376] "indianred4"           "ivory"                "ivory1"              
[379] "ivory2"               "ivory3"               "ivory4"              
[382] "khaki"                "khaki1"               "khaki2"              
[385] "khaki3"               "khaki4"               "lavender"            
[388] "lavenderblush"        "lavenderblush1"       "lavenderblush2"      
[391] "lavenderblush3"       "lavenderblush4"       "lawngreen"           
[394] "lemonchiffon"         "lemonchiffon1"        "lemonchiffon2"       
[397] "lemonchiffon3"        "lemonchiffon4"        "lightblue"           
[400] "lightblue1"           "lightblue2"           "lightblue3"          
[403] "lightblue4"           "lightcoral"           "lightcyan"           
[406] "lightcyan1"           "lightcyan2"           "lightcyan3"          
[409] "lightcyan4"           "lightgoldenrod"       "lightgoldenrod1"     
[412] "lightgoldenrod2"      "lightgoldenrod3"      "lightgoldenrod4"     
[415] "lightgoldenrodyellow" "lightgray"            "lightgreen"          
[418] "lightgrey"            "lightpink"            "lightpink1"          
[421] "lightpink2"           "lightpink3"           "lightpink4"          
[424] "lightsalmon"          "lightsalmon1"         "lightsalmon2"        
[427] "lightsalmon3"         "lightsalmon4"         "lightseagreen"       
[430] "lightskyblue"         "lightskyblue1"        "lightskyblue2"       
[433] "lightskyblue3"        "lightskyblue4"        "lightslateblue"      
[436] "lightslategray"       "lightslategrey"       "lightsteelblue"      
[439] "lightsteelblue1"      "lightsteelblue2"      "lightsteelblue3"     
[442] "lightsteelblue4"      "lightyellow"          "lightyellow1"        
[445] "lightyellow2"         "lightyellow3"         "lightyellow4"        
[448] "limegreen"            "linen"                "magenta"             
[451] "magenta1"             "magenta2"             "magenta3"            
[454] "magenta4"             "maroon"               "maroon1"             
[457] "maroon2"              "maroon3"              "maroon4"             
[460] "mediumaquamarine"     "mediumblue"           "mediumorchid"        
[463] "mediumorchid1"        "mediumorchid2"        "mediumorchid3"       
[466] "mediumorchid4"        "mediumpurple"         "mediumpurple1"       
[469] "mediumpurple2"        "mediumpurple3"        "mediumpurple4"       
[472] "mediumseagreen"       "mediumslateblue"      "mediumspringgreen"   
[475] "mediumturquoise"      "mediumvioletred"      "midnightblue"        
[478] "mintcream"            "mistyrose"            "mistyrose1"          
[481] "mistyrose2"           "mistyrose3"           "mistyrose4"          
[484] "moccasin"             "navajowhite"          "navajowhite1"        
[487] "navajowhite2"         "navajowhite3"         "navajowhite4"        
[490] "navy"                 "navyblue"             "oldlace"             
[493] "olivedrab"            "olivedrab1"           "olivedrab2"          
[496] "olivedrab3"           "olivedrab4"           "orange"              
[499] "orange1"              "orange2"              "orange3"             
[502] "orange4"              "orangered"            "orangered1"          
[505] "orangered2"           "orangered3"           "orangered4"          
[508] "orchid"               "orchid1"              "orchid2"             
[511] "orchid3"              "orchid4"              "palegoldenrod"       
[514] "palegreen"            "palegreen1"           "palegreen2"          
[517] "palegreen3"           "palegreen4"           "paleturquoise"       
[520] "paleturquoise1"       "paleturquoise2"       "paleturquoise3"      
[523] "paleturquoise4"       "palevioletred"        "palevioletred1"      
[526] "palevioletred2"       "palevioletred3"       "palevioletred4"      
[529] "papayawhip"           "peachpuff"            "peachpuff1"          
[532] "peachpuff2"           "peachpuff3"           "peachpuff4"          
[535] "peru"                 "pink"                 "pink1"               
[538] "pink2"                "pink3"                "pink4"               
[541] "plum"                 "plum1"                "plum2"               
[544] "plum3"                "plum4"                "powderblue"          
[547] "purple"               "purple1"              "purple2"             
[550] "purple3"              "purple4"              "red"                 
[553] "red1"                 "red2"                 "red3"                
[556] "red4"                 "rosybrown"            "rosybrown1"          
[559] "rosybrown2"           "rosybrown3"           "rosybrown4"          
[562] "royalblue"            "royalblue1"           "royalblue2"          
[565] "royalblue3"           "royalblue4"           "saddlebrown"         
[568] "salmon"               "salmon1"              "salmon2"             
[571] "salmon3"              "salmon4"              "sandybrown"          
[574] "seagreen"             "seagreen1"            "seagreen2"           
[577] "seagreen3"            "seagreen4"            "seashell"            
[580] "seashell1"            "seashell2"            "seashell3"           
[583] "seashell4"            "sienna"               "sienna1"             
[586] "sienna2"              "sienna3"              "sienna4"             
[589] "skyblue"              "skyblue1"             "skyblue2"            
[592] "skyblue3"             "skyblue4"             "slateblue"           
[595] "slateblue1"           "slateblue2"           "slateblue3"          
[598] "slateblue4"           "slategray"            "slategray1"          
[601] "slategray2"           "slategray3"           "slategray4"          
[604] "slategrey"            "snow"                 "snow1"               
[607] "snow2"                "snow3"                "snow4"               
[610] "springgreen"          "springgreen1"         "springgreen2"        
[613] "springgreen3"         "springgreen4"         "steelblue"           
[616] "steelblue1"           "steelblue2"           "steelblue3"          
[619] "steelblue4"           "tan"                  "tan1"                
[622] "tan2"                 "tan3"                 "tan4"                
[625] "thistle"              "thistle1"             "thistle2"            
[628] "thistle3"             "thistle4"             "tomato"              
[631] "tomato1"              "tomato2"              "tomato3"             
[634] "tomato4"              "turquoise"            "turquoise1"          
[637] "turquoise2"           "turquoise3"           "turquoise4"          
[640] "violet"               "violetred"            "violetred1"          
[643] "violetred2"           "violetred3"           "violetred4"          
[646] "wheat"                "wheat1"               "wheat2"              
[649] "wheat3"               "wheat4"               "whitesmoke"          
[652] "yellow"               "yellow1"              "yellow2"             
[655] "yellow3"              "yellow4"              "yellowgreen"         
sample(colors(),10)
 [1] "seagreen"      "royalblue1"    "slategray"     "gray88"       
 [5] "antiquewhite3" "deepskyblue2"  "hotpink1"      "chartreuse1"  
 [9] "royalblue4"    "lightyellow3" 
hist(trees$Height,col=sample(colors(),6))

hist(trees$Height,border="blue",col="pink")

hist(trees$Height,col=rainbow(3))

hist(trees$Height,col=c("blue","pink","yellow"))

hist(trees$Height,border="tomato1",breaks=c(60,70,80,90,100),col="pink")

hist(trees$Height,col=c("blue","pink","yellow","grey"))

5.4.2 Wykres pudełkowy

boxplot(trees$Height,col="red")

head(trees)
  Girth Height Volume
1   8.3     70   10.3
2   8.6     65   10.3
3   8.8     63   10.2
4  10.5     72   16.4
5  10.7     81   18.8
6  10.8     83   19.7

5.4.3 Wykresy rozrzutu

plot(trees$Height,trees$Volume)

pairs(trees)

5.4.4 Wykres słupkowy

head(chickwts)
  weight      feed
1    179 horsebean
2    160 horsebean
3    136 horsebean
4    227 horsebean
5    217 horsebean
6    168 horsebean
chickwts$feed
 [1] horsebean horsebean horsebean horsebean horsebean horsebean horsebean
 [8] horsebean horsebean horsebean linseed   linseed   linseed   linseed  
[15] linseed   linseed   linseed   linseed   linseed   linseed   linseed  
[22] linseed   soybean   soybean   soybean   soybean   soybean   soybean  
[29] soybean   soybean   soybean   soybean   soybean   soybean   soybean  
[36] soybean   sunflower sunflower sunflower sunflower sunflower sunflower
[43] sunflower sunflower sunflower sunflower sunflower sunflower meatmeal 
[50] meatmeal  meatmeal  meatmeal  meatmeal  meatmeal  meatmeal  meatmeal 
[57] meatmeal  meatmeal  meatmeal  casein    casein    casein    casein   
[64] casein    casein    casein    casein    casein    casein    casein   
[71] casein   
Levels: casein horsebean linseed meatmeal soybean sunflower
# barplot(chickwts$feed)
# Powyższy kod nie zadziała, ponieważ dane powinny być wektorem lub macierzą.

t=table(chickwts$feed)
t

   casein horsebean   linseed  meatmeal   soybean sunflower 
       12        10        12        11        14        12 
barplot(t)

5.4.5 Wykres kołowy

pie(t)

procenty=round(prop.table(t)*100,1)
procenty

   casein horsebean   linseed  meatmeal   soybean sunflower 
     16.9      14.1      16.9      15.5      19.7      16.9 
pie(t,labels=paste(names(procenty),procenty,"%"))

pie(t,labels=paste(names(t),procenty,"%"))

5.5 📘 Elementy rachunku prawdopodobieństwa

# Elementy rachunku prawdopodobieństwa: generowanie wartości z rozkładów, gęstość, dystrybuanta i kwantyle.

5.5.1 Generowanie wartości z rozkładów

?rnorm

rnorm(20)
 [1]  0.30575243  0.90790316 -0.18437878  2.54548046 -0.78177406  0.88073186
 [7]  0.76510236 -0.12566179 -1.17615129  1.23624709 -0.09380536 -3.01406685
[13]  0.54900988 -0.79733984  0.22590023 -1.01298698 -0.55615231 -0.23687068
[19]  0.84561034  1.20805643
rnorm(100,20,13)
  [1] 31.2131617 12.9948347 -2.3309168 24.2904139  9.8591086  5.9903358
  [7] 28.2472840 24.2084460 38.2481336 17.0743181 -6.6576426 16.9710040
 [13] 25.1830881 30.8176559 40.3590340 41.4683341 28.4475905  5.1716459
 [19] 19.0194284 12.0228896 36.7515845 22.2918094 26.7883087 33.8612188
 [25] 10.4716024  3.5127539 47.8131839 37.8505259 49.3081847  5.0432692
 [31] 10.8643068 23.4537320 25.5979670  6.2596628 30.4394937  8.6170744
 [37] 33.0027917 13.3571837 56.0659343 38.0843497 18.2784281 29.7966758
 [43] -4.1485361 24.8920054  2.0374419 23.1097789  7.6362133 36.2387361
 [49] 16.5404952 57.4828448 21.0318075 -3.1458879 30.8597220 13.2584648
 [55] 11.7763349 25.8854829 17.0149652  5.7738024 33.6845572  9.6119609
 [61] 26.0165372  7.1767827  6.7720959 19.1017619 15.7293421 37.0497491
 [67] 23.2652339 -6.5983083 43.8159966 17.5213335 10.5362690 31.5464974
 [73] 36.6393863 21.0040459 32.1566066 20.4074296 18.6994701  0.6751947
 [79] 18.0553168 15.6138276 40.2660622 37.6966469 11.7335525  7.7517134
 [85] 22.2643508 21.5177531 22.4259845 35.8075532 -2.1962695 38.5435823
 [91] 23.1889310 21.7039588 25.2147620 20.3470990  7.9491371 43.0537115
 [97] 24.3694408 17.1048070  9.9371449 29.4777020
rnorm(100,sd=13,mean=20)
  [1]  13.4755631   9.8593293  42.6750007   6.8467678   4.6033123  13.2586040
  [7]  27.6975232  10.5619890  10.1570009  24.9902856  31.7203602  21.6272523
 [13]  36.6916335   8.5057722  19.0673024  23.0861934   9.0800836  25.8713957
 [19]  11.5486923  -0.6825385  19.4623632  19.9243690   2.7576895  29.8769446
 [25]   7.9606653   8.5633655  22.7579592  13.7035422   7.6505165   5.0837370
 [31]   5.2338197   1.9113583   8.8054010  14.5361132  33.4771104  14.6497795
 [37]   1.4621366  43.8265455   8.3003481  13.7427920  33.2715768  39.9163717
 [43]   6.9007432   9.0622065  27.7848292  45.0902722  47.2470499 -19.4906171
 [49]  22.2797548  41.6781918  19.4475934  23.7289907  22.7181216  25.9364800
 [55]   5.9412664   5.5113149  12.6556434  30.4065820  16.8191913  19.4687880
 [61]  27.5358102  31.9348068  25.4743899   5.2363152  26.8446548  18.9913262
 [67]  24.7089201  15.5382431   7.9807663  13.2275802  38.4013136   4.9257529
 [73]  28.5900083  19.8451570  19.7725687   9.9768339  12.3554892  43.5968194
 [79]  27.5595061  43.2084072  45.6241252  -8.0224096  22.7437931   2.5865561
 [85]  16.7998918  33.6359719  23.5802236  26.1879331  -6.4215430  40.4405528
 [91]  29.2349867  20.6981865  -3.3434369  33.6263449  24.2508891  -0.3158182
 [97]  11.7347854  29.5467992  35.4645374   7.3167181
set.seed(123)
n=rnorm(100, 2,0.5)
n
  [1] 1.7197622 1.8849113 2.7793542 2.0352542 2.0646439 2.8575325 2.2304581
  [8] 1.3674694 1.6565736 1.7771690 2.6120409 2.1799069 2.2003857 2.0553414
 [15] 1.7220794 2.8934566 2.2489252 1.0166914 2.3506780 1.7636043 1.4660881
 [22] 1.8910125 1.4869978 1.6355544 1.6874804 1.1566533 2.4188935 2.0766866
 [29] 1.4309315 2.6269075 2.2132321 1.8524643 2.4475628 2.4390667 2.4107905
 [36] 2.3443201 2.2769588 1.9690441 1.8470187 1.8097645 1.6526465 1.8960414
 [43] 1.3673018 3.0844780 2.6039810 1.4384457 1.7985576 1.7666723 2.3899826
 [50] 1.9583155 2.1266593 1.9857266 1.9785648 2.6843011 1.8871145 2.7582353
 [57] 1.2256236 2.2923069 2.0619271 2.1079708 2.1898197 1.7488383 1.8333963
 [64] 1.4907123 1.4641044 2.1517643 2.2241049 2.0265021 2.4611337 3.0250423
 [71] 1.7544844 0.8454156 2.5028693 1.6453996 1.6559957 2.5127857 1.8576135
 [78] 1.3896411 2.0906517 1.9305543 2.0028821 2.1926402 1.8146700 2.3221883
 [85] 1.8897567 2.1658910 2.5484195 2.2175907 1.8370342 2.5744038 2.4967519
 [92] 2.2741985 2.1193659 1.6860470 2.6803262 1.6998702 3.0936665 2.7663053
 [99] 1.8821498 1.4867895
j=runif(100)
j
  [1] 0.238726027 0.962358936 0.601365726 0.515029727 0.402573342 0.880246541
  [7] 0.364091865 0.288239281 0.170645235 0.172171746 0.482042606 0.252964929
 [13] 0.216254790 0.674376388 0.047663627 0.700853087 0.351888638 0.408943998
 [19] 0.820951324 0.918857348 0.282528330 0.961104794 0.728394428 0.686375082
 [25] 0.052843943 0.395220135 0.477845380 0.560253264 0.698261595 0.915683538
 [31] 0.618351227 0.428421509 0.542080367 0.058478489 0.260856857 0.397151953
 [37] 0.197744737 0.831927563 0.152887223 0.803418542 0.546826157 0.662317642
 [43] 0.171698494 0.633055360 0.311869747 0.724554346 0.398939825 0.969356411
 [49] 0.967398371 0.726702539 0.257216746 0.221787935 0.593045652 0.267521432
 [55] 0.531070399 0.785291671 0.168060811 0.404399181 0.471576278 0.868106807
 [61] 0.925707956 0.881977559 0.674186843 0.950166979 0.516444894 0.576519021
 [67] 0.336331206 0.347324631 0.020024301 0.502813046 0.871043414 0.006300784
 [73] 0.072057124 0.164211225 0.770334074 0.735184306 0.971875636 0.466472377
 [79] 0.074384513 0.648818124 0.758593170 0.137106081 0.396584595 0.224985329
 [85] 0.057958561 0.395892688 0.064928300 0.225886433 0.054629109 0.670282040
 [91] 0.297741783 0.100721582 0.071904097 0.880440569 0.754247402 0.816605888
 [97] 0.982140374 0.103599645 0.099041829 0.798831611
s=rt(100,df=3)
s
  [1]  0.69683236  0.82060066 -0.02475866 -0.30644712 -0.30056295 -3.47363186
  [7] -1.31714799 -0.46532917 -0.01932117  5.99328177 -0.02021276 -2.00872529
 [13] -0.57321111 -0.16850664 -1.41785209 -1.20204135 -0.52541258  1.23078376
 [19]  0.63466850  2.34977229  1.88108475 -2.20687007  6.41947266 -0.25537575
 [25] -0.66606686 -0.01114930 -0.06244739  0.18466027 -1.25469184  0.08335478
 [31]  0.35642587 -0.53703200  1.00405279 -0.43246746 -1.34543674  1.92487880
 [37] -0.09990203 -1.26894058  0.83961497 -0.15032212 -0.83106377  0.01523773
 [43]  1.00633019 -0.12547272 -1.77088587 -3.22061623 -0.07322264 -0.50701695
 [49] -0.50295934  0.07520585  0.18176418 -0.85664567  0.67830426  1.78504381
 [55] -0.24748408  0.93705785  1.97205423  0.21457114  0.36545186  1.70894197
 [61] -0.34914733  0.93052910  4.51244483 -1.46438907  1.56468817  0.49041375
 [67]  1.11727468  0.43312514  0.29718297 -2.04567260 -1.36525725 -0.66750687
 [73] -0.49447123 -0.93744377  0.51235989 -8.61233265  0.70151938  0.89078422
 [79] -0.21608493 -0.81058160 -0.25568636 -2.63293864 -1.00076993 -3.08952378
 [85] -0.01260136 -0.20001064  0.93324733 -0.06879633  2.80205973 -0.95441015
 [91] -0.78877949  0.42289498  0.75830163  0.53165633  0.85237062  0.55751630
 [97]  0.65719967  1.41166493  0.32995741  2.43177705
c=rchisq(100,3)
c
  [1] 3.3850922 3.2984545 1.6909650 0.1576374 6.6977146 0.4255763 2.1398074
  [8] 3.0006399 3.1373579 2.7302180 5.8218036 0.4584186 1.6201983 0.7657052
 [15] 2.9739183 4.1567176 5.0755977 1.1720594 1.3637716 3.0758988 2.2844511
 [22] 3.8891418 0.6878708 6.9350646 2.1324304 4.8828211 7.9019783 1.4766519
 [29] 0.5130345 1.5948243 1.9896741 2.0411105 2.6774314 5.5385065 2.2499958
 [36] 3.6797567 3.8610315 4.2479516 1.0161754 5.9954669 2.3432680 2.7945191
 [43] 3.2567545 0.9773518 4.6550916 1.8906219 9.3182640 2.7903987 1.0009019
 [50] 2.4556660 4.1543027 2.4323302 0.9571249 2.2230586 0.3827861 0.4611069
 [57] 1.7458361 1.7893021 3.1419871 0.1678722 0.4058235 3.9225606 5.0094145
 [64] 2.7821002 0.9680566 1.3273275 1.1724402 0.9700765 4.1080274 4.1016847
 [71] 0.3211031 3.6369040 2.6853121 0.6705557 0.7415162 2.1502738 6.2488106
 [78] 2.9134959 4.3211165 1.4858849 1.6249270 2.3603811 0.6411606 0.4162545
 [85] 2.3591057 2.3395796 4.2461522 2.3558489 3.5971023 1.0379425 4.3845427
 [92] 5.5239566 0.4184004 3.5731431 2.1469375 0.1211514 0.7123071 1.8005444
 [99] 1.9840761 2.8355945
f=rf(100,df1=4,df2=5)
f
  [1]  0.52610805  1.74521305  1.02604707  3.25032204  1.52430340  0.28097148
  [7]  0.38109784  0.55076467  0.69027447  0.48196860  4.41313923  0.73094071
 [13]  0.37996535  2.06320618  0.84712631  0.61603119  0.71032146  0.62933857
 [19]  2.82465565  0.41869146  2.67819390  1.77195322  0.53829047  1.08785238
 [25]  1.95254581  1.14638625  0.27337680  0.58384781  0.33364606  0.77739386
 [31]  0.48367768  1.58395506  0.85833052  0.08154664  0.28514547  0.84480764
 [37]  2.62597743  1.21076087  2.08760690  1.89972530  1.17307090  0.21546587
 [43]  1.24627808  1.35692310 17.71356434  0.20513635  1.58029619  2.90312814
 [49]  0.07009730  1.31514070  0.00564881  3.51205181  2.68952096  1.18568879
 [55]  1.58932593  2.01802763  1.59471709  0.75218091  0.59938150  1.70882973
 [61]  1.77348471  0.28766346  0.17464260  1.10959418  0.83223825  4.74271587
 [67]  3.58385752  0.09552937  1.26651119  0.28091568  0.48236156 12.00955112
 [73]  0.69463279  0.71923276  1.15728964  1.90554090  5.86638409  0.44790960
 [79]  0.09469444  2.63703334  0.09821284  0.21453281  0.17428717  3.00294331
 [85]  0.38385209  3.40359044  0.66721172  0.69316870  1.09003637  0.85520126
 [91]  3.29537360  0.66066119  0.27395316  0.10956574  0.26362624  0.53813684
 [97]  0.24114574  0.05285393  0.37716631  0.73218773

5.5.2 Gęstość

dnorm(0)
[1] 0.3989423
dnorm(0,mean=3,sd=1)
[1] 0.004431848
dnorm(seq(-3,3,0.05))
  [1] 0.004431848 0.005142641 0.005952532 0.006872767 0.007915452 0.009093563
  [7] 0.010420935 0.011912244 0.013582969 0.015449347 0.017528300 0.019837354
 [13] 0.022394530 0.025218220 0.028327038 0.031739652 0.035474593 0.039550042
 [19] 0.043983596 0.048792019 0.053990967 0.059594706 0.065615815 0.072064874
 [25] 0.078950158 0.086277319 0.094049077 0.102264925 0.110920835 0.120009001
 [31] 0.129517596 0.139430566 0.149727466 0.160383327 0.171368592 0.182649085
 [37] 0.194186055 0.205936269 0.217852177 0.229882141 0.241970725 0.254059056
 [43] 0.266085250 0.277984886 0.289691553 0.301137432 0.312253933 0.322972360
 [49] 0.333224603 0.342943855 0.352065327 0.360526962 0.368270140 0.375240347
 [55] 0.381387815 0.386668117 0.391042694 0.394479331 0.396952547 0.398443914
 [61] 0.398942280 0.398443914 0.396952547 0.394479331 0.391042694 0.386668117
 [67] 0.381387815 0.375240347 0.368270140 0.360526962 0.352065327 0.342943855
 [73] 0.333224603 0.322972360 0.312253933 0.301137432 0.289691553 0.277984886
 [79] 0.266085250 0.254059056 0.241970725 0.229882141 0.217852177 0.205936269
 [85] 0.194186055 0.182649085 0.171368592 0.160383327 0.149727466 0.139430566
 [91] 0.129517596 0.120009001 0.110920835 0.102264925 0.094049077 0.086277319
 [97] 0.078950158 0.072064874 0.065615815 0.059594706 0.053990967 0.048792019
[103] 0.043983596 0.039550042 0.035474593 0.031739652 0.028327038 0.025218220
[109] 0.022394530 0.019837354 0.017528300 0.015449347 0.013582969 0.011912244
[115] 0.010420935 0.009093563 0.007915452 0.006872767 0.005952532 0.005142641
[121] 0.004431848
x<-rnorm(100,3,1)
hist(x,prob=T)

lx=seq(-3,9,length=120)
lx
  [1] -3.00000000 -2.89915966 -2.79831933 -2.69747899 -2.59663866 -2.49579832
  [7] -2.39495798 -2.29411765 -2.19327731 -2.09243697 -1.99159664 -1.89075630
 [13] -1.78991597 -1.68907563 -1.58823529 -1.48739496 -1.38655462 -1.28571429
 [19] -1.18487395 -1.08403361 -0.98319328 -0.88235294 -0.78151261 -0.68067227
 [25] -0.57983193 -0.47899160 -0.37815126 -0.27731092 -0.17647059 -0.07563025
 [31]  0.02521008  0.12605042  0.22689076  0.32773109  0.42857143  0.52941176
 [37]  0.63025210  0.73109244  0.83193277  0.93277311  1.03361345  1.13445378
 [43]  1.23529412  1.33613445  1.43697479  1.53781513  1.63865546  1.73949580
 [49]  1.84033613  1.94117647  2.04201681  2.14285714  2.24369748  2.34453782
 [55]  2.44537815  2.54621849  2.64705882  2.74789916  2.84873950  2.94957983
 [61]  3.05042017  3.15126050  3.25210084  3.35294118  3.45378151  3.55462185
 [67]  3.65546218  3.75630252  3.85714286  3.95798319  4.05882353  4.15966387
 [73]  4.26050420  4.36134454  4.46218487  4.56302521  4.66386555  4.76470588
 [79]  4.86554622  4.96638655  5.06722689  5.16806723  5.26890756  5.36974790
 [85]  5.47058824  5.57142857  5.67226891  5.77310924  5.87394958  5.97478992
 [91]  6.07563025  6.17647059  6.27731092  6.37815126  6.47899160  6.57983193
 [97]  6.68067227  6.78151261  6.88235294  6.98319328  7.08403361  7.18487395
[103]  7.28571429  7.38655462  7.48739496  7.58823529  7.68907563  7.78991597
[109]  7.89075630  7.99159664  8.09243697  8.19327731  8.29411765  8.39495798
[115]  8.49579832  8.59663866  8.69747899  8.79831933  8.89915966  9.00000000
lines(lx,dnorm(lx,3,1),col='red')

5.5.3 Kwantyle

qnorm(0.5)
[1] 0
qnorm(0.75,2,0.23)
[1] 2.155133
qnorm(0.95,1,2)
[1] 4.289707

5.5.4 Dystrybuanta

pnorm(0.5)
[1] 0.6914625

5.5.5 Przedstawienie kilku wykresów gęstości na 1 wykresie

z=seq(-5,5,length=120)
z
  [1] -5.00000000 -4.91596639 -4.83193277 -4.74789916 -4.66386555 -4.57983193
  [7] -4.49579832 -4.41176471 -4.32773109 -4.24369748 -4.15966387 -4.07563025
 [13] -3.99159664 -3.90756303 -3.82352941 -3.73949580 -3.65546218 -3.57142857
 [19] -3.48739496 -3.40336134 -3.31932773 -3.23529412 -3.15126050 -3.06722689
 [25] -2.98319328 -2.89915966 -2.81512605 -2.73109244 -2.64705882 -2.56302521
 [31] -2.47899160 -2.39495798 -2.31092437 -2.22689076 -2.14285714 -2.05882353
 [37] -1.97478992 -1.89075630 -1.80672269 -1.72268908 -1.63865546 -1.55462185
 [43] -1.47058824 -1.38655462 -1.30252101 -1.21848739 -1.13445378 -1.05042017
 [49] -0.96638655 -0.88235294 -0.79831933 -0.71428571 -0.63025210 -0.54621849
 [55] -0.46218487 -0.37815126 -0.29411765 -0.21008403 -0.12605042 -0.04201681
 [61]  0.04201681  0.12605042  0.21008403  0.29411765  0.37815126  0.46218487
 [67]  0.54621849  0.63025210  0.71428571  0.79831933  0.88235294  0.96638655
 [73]  1.05042017  1.13445378  1.21848739  1.30252101  1.38655462  1.47058824
 [79]  1.55462185  1.63865546  1.72268908  1.80672269  1.89075630  1.97478992
 [85]  2.05882353  2.14285714  2.22689076  2.31092437  2.39495798  2.47899160
 [91]  2.56302521  2.64705882  2.73109244  2.81512605  2.89915966  2.98319328
 [97]  3.06722689  3.15126050  3.23529412  3.31932773  3.40336134  3.48739496
[103]  3.57142857  3.65546218  3.73949580  3.82352941  3.90756303  3.99159664
[109]  4.07563025  4.15966387  4.24369748  4.32773109  4.41176471  4.49579832
[115]  4.57983193  4.66386555  4.74789916  4.83193277  4.91596639  5.00000000
plot(z,dnorm(z),type="l")
lines(z,dnorm(z,0,3),type="l",lty="dotted")
lines(z,dnorm(z,0,0.5),type="l",lty="dashed")   

# Ostatnia linia wychodzi poza obszar wykresu, ponieważ te linie dorysowywane są do wykresu, 
# czyli nie zmieniają jego rozmiaru. 
# Wykres uzyskany za pomocą funkcji plot() determinuje rozmiar wykresu na stałe. 

z=seq(-10,10,length=120)
plot(z,dnorm(z,0,1),type="l")
lines(z,dnorm(z,2,1),type="l",lty="dotted")
lines(z,dnorm(z,0,2),type="l",lty="dashed")

5.5.6 Dodawanie legendy do wykresu

plot(z,dnorm(z),type="l")
lines(z,dnorm(z,0,3),type="l",lty="dotted")
legend("topright",inset =0.01,lty=c("solid","dotted"),
       c(expression(N(mu==0,sigma==1)),expression(N(mu==0,sigma==3))) )

# Możliwe umiejscowienia legendy:  
# "bottomright"
# "bottom"
# "bottomleft"
# "left"
# "topleft"
# "top"
# "topright"
# "right" 
# "center"

5.5.7 Przykład

# Wygeneruj 100 wartości z rozkładu normalnego o średniej równej -3 i odchyleniu standardowym równym 1.
# Wygeneruj 100 wartości z rozkładu t-Studenta o 8 stopniach swobody.
# Wygeneruj 100 wartości z rozkładu Chikwadrat o 2 stopniach swobody.
# Przedstaw histogramy dla wygenerowanych wartości na 1 wykresie jeden obok drugiego.


x=rnorm(100,-3,1)
y=rt(100,8)
z=rchisq(100,2)
par(mfrow=c(1,3))
hist(x)
hist(y)
hist(z)