import seaborn as sns
import matplotlib.pyplot as plt
df = sns.load_dataset('tips')
print(df.shape)
print(df.head(3))
sns.violinplot(data=df, x='day', y='total_bill', hue='sex', split=True); plt.show()

# Data setup
import warnings; warnings.filterwarnings('ignore')
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# For data preview later
sns.set(style='whitegrid')

# Uniform Distribution - Simulating Random Decimal Numbers
uniform_data = np.random.uniform(0, 10, 1000)

plt.figure(figsize=(7,4))
sns.histplot(uniform_data, bins=20, kde=True, color='skyblue')
plt.title('Uniform Distribution (0 to 10)')
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.show()

# Uniform Distribution: Everyday Example
from scipy.stats import uniform

prob = uniform.cdf(3, loc=0, scale=10)
print(f"Probability that X < 3 when X is uniform between 0 and 10: {prob:.2f}")

# Simulating Heights Using Normal Distribution
heights = np.random.normal(loc=170, scale=10, size=1000)

plt.figure(figsize=(7,4))
sns.histplot(heights, bins=30, kde=True, color='orchid')
plt.title('Simulated Heights (Normal Distribution, mean=170, sd=10)')
plt.xlabel('Height (cm)')
plt.ylabel('Number of People')
plt.show()

# Normal Probability Example
from scipy.stats import norm

prob_180 = norm.cdf(180, loc=170, scale=10)
print("Probability that height is less than 180 cm:", round(prob_180, 3))

prob_190 = norm.cdf(190, loc=170, scale=10)
print("Probability that height is less than 190 cm:", round(prob_190, 3))

# Visualizing Normal Distribution with Mean and Spread
x = np.linspace(140, 200, 500)
for mu, sigma, color in [(170, 10, 'orchid'), (170, 20, 'deepskyblue'), (180, 10, 'coral')]:
    y = norm.pdf(x, mu, sigma)
    plt.plot(x, y, label=f"mean={mu}, sd={sigma}", color=color)

plt.title('Normal Distribution: Changing Mean and SD')
plt.xlabel('Value')
plt.ylabel('Probability')
plt.legend()
plt.show()

# Exponential Distribution - Simulate Waiting Times
wait_times = np.random.exponential(scale=5, size=1000)

plt.figure(figsize=(7,4))
sns.histplot(wait_times, bins=30, kde=True, color='limegreen')
plt.title('Exponential Distribution (mean waiting time = 5)')
plt.xlabel('Waiting Time (minutes)')
plt.ylabel('Frequency')
plt.show()

# Probability of Waiting Less Than 3 Minutes
from scipy.stats import expon

prob_less_3 = expon.cdf(3, scale=5)
print("Probability wait is less than 3 minutes:", round(prob_less_3, 3))

prob_more_10 = 1 - expon.cdf(10, scale=5)
print("Probability wait is over 10 minutes:", round(prob_more_10, 3))

# Comparing Distributions on One Plot
x = np.linspace(0, 20, 500)
plt.figure(figsize=(8,5))
plt.plot(x, uniform.pdf(x, loc=0, scale=10), label='Uniform(0,10)', color='deepskyblue')
plt.plot(x, norm.pdf(x, loc=10, scale=3), label='Normal(mean=10, sd=3)', color='orchid')
plt.plot(x, expon.pdf(x, scale=5), label='Exponential(mean=5)', color='limegreen')
plt.title('Uniform vs Normal vs Exponential Distributions')
plt.xlabel('Value')
plt.ylabel('Probability')
plt.legend()
plt.show()

# Simulate Customer Arrivals (like exponential process)
np.random.seed(42)
arrivals = np.random.exponential(scale=5, size=60)
arrival_times = np.cumsum(arrivals)
df = pd.DataFrame({'Minutes': np.arange(1, 61), 'Time_of_Arrival': arrival_times})
df['Time_of_Arrival'] = df['Time_of_Arrival'].round(2)
print(df.head())

# Plotting Arrival Pattern
plt.figure(figsize=(8,4))
plt.plot(df['Minutes'], df['Time_of_Arrival'], marker='o', color='purple')
plt.title('Cumulative Arrival Times Over One Hour')
plt.xlabel('Minute')
plt.ylabel('Arrival Time (minutes)')
plt.show()

# Practice: Predict the Next Arrival
next_minute = int(input("Guess the minute the next customer arrives after minute 60: "))
if next_minute > 60 and next_minute < 80:
    print("Great guess! That is within a realistic range for this shop.")
else:
    print("Interesting guess! Keep an eye on how exponential randomness works.")
    

# Challenge: Which Distribution Should I Use?
scenario = input("You are asked to model the height of a random person. Which distribution fits best? (uniform, normal, exponential): ")
if scenario.lower() == 'normal':
    print("Correct! People\'s heights usually follow a normal curve.")
else:
    print("Try again. Think of shapes like bell curves versus even or waiting time.")
    

# Best Practices: Choosing a Distribution

# - Uniform: Any value in a range is equally likely (e.g., random PIN).
# - Normal: Values bunch up near average, fewer outliers (e.g., heights).
# - Exponential: Chance drops off over time, no true maximum (e.g., waiting times).

# When unsure, draw a histogram of your data first!