Appendix - Introduction

x = 10             # assign x the value 10
print(x)           # print x

y = c(1,3,5,7,9)          # create vector using c()
print(y)
print(y[3])               # calling 3rd element (R indices start at 1)
print(dim(y))             # gives NULL since y is a vector, not a matrix
print(length(y))          # as expected, y has length 5
v = matrix(nrow=2,ncol=3) # fill a 2 x 3 matrix with NaN values (default)
print(dim(v))             # as expected, v is size (2,3)
w = matrix(c(1,2,3),nrow=6,ncol=3) # repeats matrix twice by rows, thrice by columns
print(w)
s = 1:10                  # s is a list of integers from 1 to 10 inclusive
print(s)                  

y = [1,3,5,7,9]       # lists in square brackets are stored as arrays
print(y)
print(y[2])           # 3rd element (Python indices start at 0)
print(len(y))         # as expected, y has length 5
import numpy as np    # NumPy: Numeric Python package
v = np.full([2,3], np.nan) # create a 2x3 matrix with NaN values
print(v)           
print(v.shape)        # as expected, v is size (2,3)
w = np.tile([1,2,3], (3,2)) # repeats thrice by rows, twice by columns
print(w)
s = range(10)         # an iterator from 0 to 9
print([x for x in s]) # return  elements using list comprehension

y=matrix(c(3.1,4.15,9))
sum(y)         # sum of all elements of y
prod(y)        # product of all elements of y
max(y)         # maximum value of y
min(y)         # minimum value of y
range(y)       # min, max value of y
mean(y)        # arithmetic mean
median(y)      # median
var(y)         # variance
cov(y)         # covar matrix = variance for single vector
cor(y)         # corr matrix = [1] for single vector
sort(y)        # sorting in ascending order
log(y)         # natural log

import numpy as np
y = [3.14, 15, 9.26, 5]
print(sum(y))          # sum of all elements of y
print(max(y))          # maximum value of y
print(min(y))          # minimum value of y
print(np.mean(y))      # arithmetic mean
print(np.median(y))    # median
print(np.var(y))       # population variance
print(np.cov(y))       # covar matrix = sample variance for single vector
print(np.corrcoef(y))  # corr matrix = [1] for single vector
print(np.sort(y))      # sort in ascending order
print(np.log(y))       # natural log

library(moments)
mean(y)      # mean
var(y)       # variance
sd(y)        # unbiased standard deviation, by default
skewness(y)  # skewness
kurtosis(y)  # kurtosis

from scipy import stats
print(np.mean(y))                        # mean
print(np.var(y))                         # variance
print(np.std(y, ddof = 1))               # ddof = 1 for unbiased standard deviation
print(stats.skew(y))                     # skewness
print(stats.kurtosis(y, fisher = False)) # fisher = False gives Pearson definition

z = matrix(c(1,2,3,4),2,2)   # z is a 2 x 2 matrix
x = matrix(c(1,2),1,2)       # x is a 1 x 2 matrix
z %*% t(x)                   # this evaluates to a 2 x 1 matrix
rbind(z,x)                   # "stacking" z and x vertically
cbind(z,t(x))                # "stacking z and x' horizontally

z = np.matrix([[1, 2], [3, 4]])                   # z is a 2 x 2 matrix
x = np.matrix([1, 2])                             # x is a 1 x 2 matrix
print(z * np.transpose(x))                        # this evaluates to a 2 x 1 matrix          
b = np.concatenate((z,x), axis = 0)               # "stacking" z and x vertically
print(b)
c = np.concatenate((z,np.transpose(x)), axis = 1) # "stacking" z and x horizontally
print(c)

q = seq(from = -3, to = 3, length = 7)     # specify a set of values
p = seq(from = 0.1, to = 0.9, length = 9)  # specify a set of probabilities
qnorm(p, mean = 0, sd = 1)                 # element-wise inverse Normal quantile
pt(q, df = 4)                              # element-wise cdf under Student-t(4)
dchisq(q, df = 2)                          # element-wise pdf under Chisq(2)
x = rt(100, df = 5)                        # Sampling 100 times from TDist with 5 df
y = rnorm(50, mean = 0, sd = 1)            # Sampling 50 times from a standard normal 
library(MASS)
res = fitdistr(x, densfun = "normal")      # Fitting x to normal dist
print(res)

q = np.arange(-3,4,1)        # specify a set of values, syntax arange(min, exclusive-max, step)
p = np.arange(0.1,1.0,0.1)   # specify a set of probabilities
print(stats.norm.ppf(p))     # element-wise inverse Normal quantile
print(stats.t.cdf(q,4))      # element-wise cdf under Student-t(4)
print(stats.chi2.pdf(q,2))   # element-wise pdf under Chisq(2)
x = np.random.standard_t(df=5, size=100)   # Sampling 100 times from TDist with 5 df
y = np.random.normal(size=50)              # Sampling 50 times from a standard normal 
res = stats.norm.fit(x)                    # Fitting x to normal dist
print(res)                                 # First element is mean, second sd

library(tseries)
x = rt(500, df = 5)                            # Create hypothetical dataset x
jarque.bera.test(x)                            # Jarque-Bera test for normality
Box.test(x, lag = 20, type = c("Ljung-Box"))   # Ljung-Box test for serial correlation

from statsmodels.stats.diagnostic import acorr_ljungbox
x = np.random.standard_t(df=5, size=500)  # Create dataset x
print(stats.jarque_bera(x))               # Jarque-Bera test - prints statistic and p-value
print(acorr_ljungbox(x, lags=20))         # Ljung-Box test - prints array of statistics and p-values

x = rt(60, df = 5)  # Create hypothetical dataset x
par(mfrow=c(1,2), pty='s')
acf(x,20)           # autocorrelation for lags 1:20
pacf(x,20)          # partial autocorrelation for lags 1:20

import statsmodels.api as sm
import matplotlib.pyplot as plt
y = np.random.standard_t(df = 5, size = 60)   # Create hypothetical dataset y
q1 = sm.tsa.stattools.acf(y, nlags=20)        # autocorrelation for lags 1:20
plt.bar(x = np.arange(1,len(q1)), height = q1[1:])
plt.show()
plt.close()
q2 = sm.tsa.stattools.pacf(y, nlags=20)       # partial autocorr for lags 1:20
plt.bar(x = np.arange(1,len(q2)), height = q2[1:])
plt.show()
plt.close()

for (i in 3:7)        # iterates through [3,4,5,6,7]
    print(i^2)      
X = 10
if (X %% 3 == 0) {
    print("X is a multiple of 3")
} else {
    print("X is not a multiple of 3")
}
excess_kurtosis = function(x, excess = 3){ # note: excess optional, default=3
    m4 = mean((x-mean(x))^4)
    excess_kurt = m4/(sd(x)^4) - excess
    excess_kurt
}
x = rt(60, df = 5)                         # Create hypothetical dataset x
excess_kurtosis(x)      

for i in range(3,8):      # NOTE: range(start, end), end excluded
    print(i**2)           # range(3,8) iterates through [3,4,5,6,7)
X = 10
if X % 3 == 0:
    print("X is a multiple of 3")
else:
    print("X is not a multiple of 3")
def excess_kurtosis(x, excess = 3):        # note: excess optional, default = 3
    m4=np.mean((x-np.mean(x))**4)          # note: exponentiation in Python uses **
    excess_kurt=m4/(np.std(x)**4)-excess
    return excess_kurt
x = np.random.standard_t(df=5,size=60)     # Create hypothetical dataset x
print(excess_kurtosis(x))

y = rnorm(50, mean = 0, sd = 1)
par(mfrow=c(2,2)) # sets up space for subplots
barplot(y)        # bar plot
plot(y,type='l')  # line plot
hist(y)           # histogram
plot(y)           # scatter plot

y = np.random.normal(size = 50)
z = np.random.standard_t(df = 4, size = 50)
plt.subplot(2,2,1)
plt.bar(range(len(y)), y);
plt.subplot(2,2,2)
plt.plot(y);
plt.subplot(2,2,3)
plt.hist(y);
plt.subplot(2,2,4)
plt.scatter(y,z);

x = 8.0
print(typeof(x))
x = as.integer(x)
print(typeof(x))

x = 8.0
print(type(x))
x = int(x)
print(type(x))