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import pandas as pd

samples = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/Advanced+Probability+course+media/expon_samples.csv', names=['Value'])
# Calculate mean value over samples
estim_mean = samples.mean()['Value']
# We know that samples are from exponential distribution with has parameter lambda.
# We also know that mean  value of exponentially distributed variable equals 1/lambda
# So to estimate lambda using momentum method we can simple use 1/estim_mean
print('Momentum estimation of lambda parameter is: ', 1/estim_mean)

              
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import pandas as pd

samples = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/Advanced+Probability+course+media/gaussian_samples.csv', names=['Value']) 

# Estimate the mean and standard deviation using method of moments
mu = samples.mean()['Value']
sigma = samples.std()['Value']

print('Estimated mean:', mu)
print('Estimated standard deviation:', sigma)

              
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import pandas as pd
from scipy.stats import norm

# Generate some random data
samples = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/Advanced+Probability+course+media/gaussian_samples.csv', names=['Value'])

# Estimate the parameters using maximum likelihood
mu_ml, sigma_ml = norm.fit(samples)

print('Maximum likelihood estimates:')
print('mu = ', mu_ml)
print('sigma = ', sigma_ml)

              
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import numpy as np
import pandas as pd
from scipy.stats import poisson
from scipy.optimize import minimize
samples = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/Advanced+Probability+course+media/pois_samples.csv', names=['Value'])

# Define the log-likelihood function for a Poisson distribution
def poisson_log_likelihood(params, data):
    lam = params[0]
    # Compute log-likelihood as sum of logarithms of Poisson PMF
    log_likelihood = -np.sum(poisson.logpmf(data, lam))
    return log_likelihood

# Use maximum likelihood estimation to fit a Poisson distribution to the data
initial_guess = [5] # starting value for lambda parameter
result = minimize(poisson_log_likelihood, initial_guess, args=samples)
estimate_lambda = result.x[0]

# Print the estimated value of lambda
print('Estimated value of lambda:', estimate_lambda)