#================================================================================================================#
#========== Jacek Wallusch ==========#
#========== MATHEMATICAL STATISTICS ==========#
#========== Lecture 5: Empirical Probability Distribution: Histogram and Kernel Density ==========#
#================================================================================================================#
#-----------------------------------------------------------------------------------------------------------------
# THE DATA:
# Federal Reserve Bank of New York: https://www.newyorkfed.org/microeconomics/sceindex
# variables: [1] Percent chance 12 months from now unemployment rate higher
# [2] Percent chance 12 months from now interest rate on savings account higher
# time: January 2016
# WARNING: don't forget to change the location of the file!!!
us_exp <- read.csv("C:/Documents and Settings/User/Moje dokumenty/WALLUSCH/Wallusch-Datenbank.de/matstat/fedny.csv",
header = TRUE, sep = ";")
q4_fed <- us_exp[,1]
q5_fed <- us_exp[,2]
#-----------------------------------------------------------------------------------------------------------------
# HISTOGRAM:
# basic graph
hist(q5_fed)
# density plotted against the bins
hist(q4_fed, freq = FALSE)
# extracting the data: [1] counts for bins [2] densities for bins [3] midpoints for bins
hist(q4_fed)$counts
hist(q4_fed)$density
hist(q4_fed)$mids
#-----------------------------------------------------------------------------------------------------------------
# KERNEL DENSITY:
# summary table
density(q4_fed)
# basic graph
plot(density(q4_fed))
# extracting the data
density(q4_fed)$x
density(q4_fed)$y
#-----------------------------------------------------------------------------------------------------------------
# slightly nicer plot
# package: PLOTLY
library(plotly)
# graph:
plot_ly(x = density(q4_fed)$x, y = density(q4_fed)$y, type = "scatter", mode = "lines")%>%
layout(xaxis = list(title = "values"),
yaxis = list(title = "density"))