# -*- coding: utf-8 -*-
"""
Created on Thu Nov 25 20:00:01 2021

@author: TANISH
"""


""" Python is Case sensitive """
# For Python, small letters are not equal to capital letters
# For eg, "n" is NOT equal to "N"

# For Binomial Distribution, as X ~ Bin(n,p)
n = 5
p = 0.1

print("n = ",n)
print("N = ",N)

print("p = ",p)
print("P = ",P)

# We certainly get an error because we have defined the 
# parameters "n" and "p" and not "N" and "P"

N = 10
P = 0.4

print("n = ",n)
print("N = ",N)

print("p = ",p)
print("P = ",P)

# We see that the output for "p" , "n" are different as of
# "P" and "N"


""" Creating Python Variables """
# All variable should start with _ or alphabets and continue with
# alphabets or numbers

# No special characters allowed (except "_")
# No "." allowed


""" Python overwrites variable """
# If a variable with a certain name is already available
# in the enviroment of Python and the same name is alotted to 
# a new expression / dataset then Python will delete all the 
# contents of the variable had previously and will store
# the new information

# For Gamma Distribution
alpha = 2
lamda = 0.4


# For Exponential Distribution
lamda = 0.25

print(lamda)

# We see that, lamda which was having a floating value of 0.4
# Now has a floating value of 0.25


""" Python follows BODMAS rule """
# That is, all expressions within () will be solved first, giving
# them the highest priority

# Calculate the Cumulative density function for,
# x = 0.1 where X ~ U(a = 0, b = 5)
x = 0.5
a = 0
b = 5

x - a / b - a
# Here we see that, the division a / b takes place first

(x - a) / (b - a)
# Here (x - a) and (b - a) are calculated first and then
# the division takes places


""" Numeric Operations """

# Addition
# To add 2 or more numbers (floating, integer, ...)
# We use "+" to add numbers

# An obs which was notes as 56 kgs by the agent during a survey
# was actually 2 kg less

weight_reported = 56
true_weight = (56 + 2)


# Subraction
# We use "-" to Subtract numbers

# Find the deviation of the observation from its mean
obs = 56
mean = 46

deviation = obs - mean


# Multiplication
# We use "*" to multiply numbers

# Calculate Variance of X, X ~ Bin(n = 10, p = 0.44567)
n = 10
p = 0.44567

variance = n * p * (1 - p)
print(variance)

# Division & Power
# We use "/" and "**" as to divide and calculate 
# the power respectively

# Calculate Variance of X, X ~ U(0,15)
a = 0
b = 15

variance = ((b - a) ** 2) / 12
print(variance)

# Again, we see that Python has overwritten the previous
# information available in the variable "variance


# Modulo
# Modulo gives the remainder after performing the division
# between 2 numbers

# A Statistician wants to fit 2 MVN distribution,
# one using 13 of 21 variables in dataset
# What no. of variables will be used to fit the 2nd MVN?

variables_left = 21 % 13
print(variables_left)


""" Working on Strings """
# In Pyhton, we write all characters / strings in "<String>"

print("Normal Distribution is Symmetric in nature")
print("SNV is a special case of Normal Distribution")

# Use "+" to concatenate 2 or more strings
print("MLE" + " is a method of estimation")


string_1 = print("Normal Distribution is Symmetric in nature")
string_2 = print("SNV is a special case of Normal Distribution")

string_1 + string_2
# The above command gives an error because "+" is used to
# concatenate 2 strings and NOT 2 print() statements
 

# Alternative way to concatenate strings
string_1 = "Normal Distribution is Symmetric in nature"
string_2 = "SNV is a special case of Normal Distribution"

print(string_1,string_2,sep = " & ")

# The sep = " " argument can be used to seperate two or more
# strings with any given delimiter
# For eg, ","  "."  "/"  "|"  etc...


# Print a string on 2 or more different lines
# We use "\n" to take the remainder of string, after \n
# to print on a new line

print("Normal Distribution is /n Symmetric in nature")


# How to use String and a variable in print()
mu = 5
sigma = 0.9

print("Mean = ",mu,"sigma = ",sigma)
print("mu = ",mu,"\t sigma = ",sigma)

# "\t" is used as a tab separater


# At times, we want to import data by providing the Path,
# However, for eg, "C:\tanish" in which the "\t" will act as a 
# tab and not a part of the Location

# Use "r" before the start of the string to make the string as a
# raw string

path_to_import_data = "\tanish\Desktop\Climate.csv"
print(path_to_import_data)

path_to_import_data = r"\tanish\Desktop\Climate.csv"
print(path_to_import_data)


# Extracting a particular part of String
# In Python, indexing starts with 0

Name = "FGM Distribution"
# Therefore,
# F G M     D I S T R I  B U  T  I  O  N
# 0 1 2  3  4 5 6 7 8 9 10 11 12 13 14 15
#                         ...   -3  -2  -1
# Each space is also alloted 1 index value


Name[0:6]

# Interpretation for above command
# Python considers 0:6 as 0 to 5, i.e [0,6) i.e [0,5]
# That is <x> : <y> = <x> : <y - 1>
# Hence, 0:6 is equal to 0 1 2 3 4 5

# We can use a negative Index to extract elements
# from back to front

Name[-1]


""" Logical Operations """
# We see how to work with Boolean values
# Or Logical values like: True / False

# Eg,
# An Actuary is trying to Model the distribution of Claim amounts
# He assumes the distribution to be Exponential

# He used 2 methods to estimate the parameters
# 1.) Method of Moments
# 2.) Maximum Likelihood Estimation

# He wants to know how both these estimates actually
# differs from each other


import random

lambda_mom = random.uniform(0.5,1.5)
lambda_mle = random.uniform(0.5,1.5)

# Equal To (==)
lambda_mle == lambda_mom

# Not Equal To (!=)
lambda_mle != lambda_mom

# Greater Than (>)
lambda_mle > lambda_mom

# Greater Than Or Equal (>=)
lambda_mle >= lambda_mom

# Less Than (<)
lambda_mle < lambda_mom

# Less Than Or Equal (<=)
lambda_mle <= lambda_mom


# Eg.
# The Actuary has given 3 papers in his previous attempts
# for which the results are out just now

# He has downlaoded the results and will decide to party if,

result_1 = random.choice(["P","F"])
result_2 = random.choice(["P","F"])
result_3 = random.choice(["P","F"])


# Use of AND operator (& / and)
# NO parties if he don't pass in any 1 of them
(result_1 == "P") and (result_2 == "P") and (result_3 == "P")
(result_1 == "P") & (result_2 == "P") & (result_3 == "P")

# Use of OR operator (| / or)
# He will party if he pass in any one of them 
(result_1 == "P") | (result_2 == "P") | (result_3 == "P")
(result_1 == "P") or (result_2 == "P") or (result_3 == "P")


# Use of NOT operator (not)
# NOT take an value opposite of the true Boolean value
# Eg, NOT will make True equal to False and vice versa

# He will party irrespective of the results
# The above question is covered in Quiz at the end of the script


""" List """

# List is one of the Data Structures which is Mutable
# Mutable means that once created, alterations / modifications
# can be made

# A List can hold multiple data types and data structures together
# even in Nested forms


distributions_list = ["Gamma","Normal","Chi-sq","Students-t","F"]
# All strings


distributions_list = ["Gamma",True,0.125]
# Mix of, String, Boolean, Numeric


# Assigment / Changing elements
distributions_list[0] = "FGM"

# Recall: Indexing starts with 0
# Syntax to create a list
# <variable> = []
# use "," to separate elements

# Extracting elements from list using Indexes
distributions_list[0]

# Adding more elements in a list
# Using "+"
distributions_list = distributions_list + ["MNV"]

# Using the append() function
distributions_list.append("MNV")

# Removing an element from list

# pop() takes only indexes and remove elements based on indexes
distributions_list.pop(0)

# remove() takes only the name of an element
distributions_list.remove("Gamma")

list_to_remove = ["Gamma","MVN"]
# We cannot directly use multiple elements in pop() remove()
# to remove multiple items from a list


# Sorting a list
# Ascending Order
distributions_list.sort() 

# Descending Order
distributions_list.sort(reverse = True)


""" Tuple """

# Tuple's are Immutable, i.e once created they cannot
# be altered or modified

# Syntax for creating a Tuple
# <var> = (,,)
# Use "," to seperate elements

distributions_tuple = ("Gamma","Normal","Chi-sq","Students-t","F")

# Extracting elements from Tuple using indexing
distributions_tuple[0]

# Check-1: Tuple's are Immutable
distributions_tuple.append("MVN")

# Check-2: Tuple's are Immutable
distributions_tuple[0] = "FGM"


# Sorting a Tuple without changing it
sorted(distributions_tuple, reverse = False)

# Gives an output of sorted elements

# Check-3: Tuple's are Immutable
distributions_tuple.sort()


# Eg.
# Creation of a List within a Tuple and other Data Types

dummy = (1,True,"str",[1,2])
# Numeric, Boolean, String, List


""" Dictonary """

# Another data structure, having the Key-Value pair format
# All keys has to be unique

# Syntax to create a Dictionary
# <var> = {<key-1> : <value-1> , ...}

# Eg.
# We have a set of 100 emails, and we count how many unique words
# has repeated (frequency) in those 100 emails and below are the
# top 5 words

bag_of_words = {"good" : 11,
                "meeting" : 13,
                "a" : 14,
                "hi" : 44,
                "Dear" : 20}

# Check: ALl key has to be unique
bag_of_words["good"] = 44

# Adding elements to a Dictionary
bag_of_words["schedule"] = 12

# Deleting a particular Key-Value pair
del bag_of_words["good"]


"""" Set """

# Another Data Structure in Python, similar to the "set" in Maths
# Set: a collection of items / elements
# A Set can only contain unique values at all times

# Syntax to create a set
# <var> = {,,} 
# set()

# Creating a Set
li = [0,2]
even_no = set(li)
even_no = {0,2,4,6,8,10}

perfect_squares = {1,4,9,16,25,36,49,64,81,100}

# Add an elements into a Set
even_no.add(12)


# Discard / Remove an element from a Set
even_no.discard(12)
# Based on values and not Index

# Union
# Gets all unique values among the 2 or more Sets
even_no.union(perfect_squares)


# Intersection
# Gets only the values which are in common among the 2 or more Sets
even_no.intersection(perfect_squares)


# Difference
# Removing elements from <Set 1> that are present in <Set 2> (say)
even_no - perfect_squares
perfect_squares - even_no 


# Subset
# To check is some element(s) is/are a part of a Set
{4}.issubset(even_no)


# Superset
# Set which has another Set included in it
even_no.issuperset({4})
{4}.issuperset(even_no)


# Set are not Subscriptable
# That is indexing do not work with Sets

# Check:
even_no[0:2]


""" Class Excercise """

# Classify the following variable as Valid / Invalid

_Var1 = ""     #Valid
Var_2. = ""    # Invalid: "."
Var3_ = ""     # Valid
Var4& = ""     # Invalid: "&"
5Var = ""      # Invalid: "5" at start
V6 = ""        # Valid


# Identify the type of variables below

distribution = "Weibull"     # String
no_of_parameters = "2"       # String
alpha = 2                    # Int
lamda = 0.4567               # Float


# Alternative Check

type(distribution)
type(no_of_parameters)
type(alpha)
type(lamda)


# Write down the output of the below expressions,

print("Error..." * 3)

"Random Forest can be used for Classification"[:-1]
"Random Forest can be used for Classification"[-1:]
"Random Forest can be used for Classification"[4:-1]

alpha = beta = theta = 0.145


""" Quiz """

# Q1.) Calculate AND print the squared deviations of the 
#      following obs: 23, 32, 26
# Answer:
obs = [23,32,26]
mean = (obs[0] + obs[1] + obs[2]) / len(obs)

squared_deviations = list()
squared_deviations.append((obs[0] - mean)**2)
squared_deviations.append((obs[1] - mean)**2)
squared_deviations.append((obs[2] - mean)**2)

print(squared_deviations)


# Q2.) Print Symmetric Distribution from,
#      "Normal Distribution is Symmetric in nature"
# Answer:
string = "Normal Distribution is Symmetric in nature"
print(string[23:32], string[7:19], sep = " ")    
# OR
print(string[22:32], string[7:19], sep = " ")    

    
# Q3.) An Actuary has 984 chocolates which he wants to distributes 
#      among his 456 friends on his Birthday
#      He wonders, how many minimum chocolates will be left if
#      all his friends are given equal no. of chocolates
# Answer:
leftover = 984 % 456
print("The Actuary has",leftover," no. of leftover chocolates")
    

# Q4.) Later, he found that he's bag can only accomodate 
#      (((59**3 - 40) // 66) // 110) chocolates.
#      Comment on the same.
# Answer:
bag_capacity = (((59**3 - 40) // 66) // 110)
decision = leftover <= bag_capacity
    
print("Can the Actuary accomodate the leftover chocolates? :",decision)


# Q5.) The Actuary has given 3 papers in his previous attempts
#      for which the results are out just now,
#      He decides that he will party irrespective of the 
#      (You are suppose to use the results of all 3 papers)
# Answer:
import random
result_1 = random.choice(["P","F"])
result_2 = random.choice(["P","F"])
result_3 = random.choice(["P","F"])

not(((result_1 == "P") & (result_2 == "P") & (result_3 == "P")) &
         ((result_1 == "F") & (result_2 == "F") & (result_3 == "F")))