Coding - Stream Sampling & Distribution Verification

`python from collections import Counter from scipy import stats # This is a bonus, showing knowledge of statistical libraries

def verify_sampling(n: int, k: int, num_trials: int = 100000): """ Verifies the uniformity of Reservoir Sampling. n: Total size of the stream (e.g., numbers from 0 to n-1 in the stream) k: Sample size num_trials: Number of simulations """ counts = Counter()

for _ in range(num_trials):
    # Generate a new stream (0 to n-1) for each trial
    stream = iter(range(n))
    sample = reservoir_sampling(stream, k)
    for num in sample:
        counts[num] += 1
        
# --- Analyze Results ---
print(f"Total elements: {n}, Sample size: {k}, Trials: {num_trials}")

expected_count = num_trials * (k / n)
print(f"Expected count per element: {expected_count}")

# Prepare data for Chi-Square Test
observed_frequencies = []
expected_frequencies = []

max_error = 0

print("\n--- Sample Frequencies ---")
# Check the frequency of each number (0 to n-1)
for i in range(n):
    obs = counts[i]
    observed_frequencies.append(obs)
    expected_frequencies.append(expected_count)
    
    error_pct = abs(obs - expected_count) / expected_count * 100
    max_error = max(max_error, error_pct)
    
    if i < 5  i > n - : 
        ()
        
()





chi2_stat, p_val = stats.chisquare(f_obs=observed_frequencies, f_exp=expected_frequencies)

()
()
()

 p_val > :
    ()
:
    ()

`