??Ask ChatGPT: <<Learn Python>> ?? Give a summary of rules found using Numerical Pattern Analysis & Benford's Law, for FRAUD ?? - with Python code??

Summary of Key Rules for Detecting Fraud Using Numerical Pattern Analysis

<<Excellent Python code below for advanced users, forensics, auditors, financial analysis>>

Numerical Pattern Analysis is a powerful method for uncovering financial anomalies and fraudulent activities. Techniques like Benford’s Law, digit frequency analysis, and distribution-based detection rely on numerical inconsistencies to highlight suspicious data.

Here are the key rules and patterns that can help detect fraud:

1. Benford’s Law Rule (Leading Digit Rule)

<<Global rule - checks all numbers?? clusters by 1st digits >>

• Description: In naturally occurring datasets, lower digits (1, 2, 3) appear more frequently as the leading digit in numbers than higher digits (8, 9).
• Fraud Indicator: If the distribution deviates significantly from Benford’s expected distribution, it may indicate manipulated data. Example: Frequent invoices starting with ‘8’ or ‘9’ may point to fabricated amounts.

? Common Use Cases: Financial statement audits, tax evasion detection, and election fraud analysis.

2. Rounded Numbers Rule

• Description: Fraudulent entries often use rounded figures to make numbers appear “clean” (e.g., $1,000, $5,000).
• Fraud Indicator: An unusually high frequency of transactions ending in ‘00’ or ‘000’ may suggest fabricated entries or manipulated rounding.

? Common Use Cases: Expense reports, payroll records, and contract value reviews.

3. Duplicate Transactions Rule

• Description: Fraudsters may create identical entries to process duplicate payments or inflate expenses.
• Fraud Indicator: Identical amounts on the same date, especially with the same vendor or account number, raise suspicion.

? Common Use Cases: Accounts Payable (A/P) and reimbursement claims.

4. Threshold Manipulation Rule

• Description: Fraudsters often structure transactions just below approval limits to bypass scrutiny.
• Fraud Indicator: Multiple transactions slightly below an internal control threshold (e.g., $9,950 for a $10,000 approval limit).

? Common Use Cases: Vendor payments, procurement, and invoice fraud.

5. Inconsistent Number Patterns Rule

• Description: Real data tends to exhibit varied digit patterns, while fabricated data often follows predictable or repetitive patterns.
• Fraud Indicator: Frequent repeating digits (e.g., $11,111) or unnatural sequences (e.g., $1234, $5678) suggest manipulation.

? Common Use Cases: Payroll systems, POS data, and procurement fraud.

6. Low-Frequency Digit Patterns Rule

• Description: Fraudsters may avoid starting numbers that they believe will attract attention, such as 1 or 2.
• Fraud Indicator: A significant underrepresentation of low digits in financial entries.

? Common Use Cases: Tax return filings and financial statements.

7. Weekend and Holiday Transactions Rule

• Description: Fraudsters may process suspicious transactions during low-oversight periods, such as weekends or holidays.
• Fraud Indicator: An unusual spike in transactions on non-business days.

? Common Use Cases: Payroll fraud, POS manipulation, and emergency fund disbursements.

8. Outlier Analysis Rule

• Description: Extreme outliers in transaction amounts may indicate intentional misreporting or fraudulent entries.
• Fraud Indicator: A cluster of extremely high or low transactions inconsistent with typical business activity.

? Common Use Cases: Vendor payments, refunds, and journal entries.

9. Unusual Vendor Behavior Rule

• Description: Fraudulent vendors often appear in limited records with suspiciously regular transaction patterns.
• Fraud Indicator: Vendors with high transaction frequency but no clear business description.

? Common Use Cases: Accounts Payable, expense claims, and procurement.

10. Irregular Time Patterns Rule

• Description: Fraudsters may manipulate financial entries during off-hours or during control gaps.
• Fraud Indicator: Multiple entries logged during early mornings, late evenings, or unexpected hours.

? Common Use Cases: POS systems, cashier overrides, and employee expense manipulation.

Best Practices for Implementing Numerical Pattern Analysis

? Combine Benford’s Law with threshold analysis and time-based patterns for improved detection accuracy.

? Use tools like Excel VBA, Python (pandas, numpy), and Power BI for automated fraud detection reporting.

? Prioritize high-risk transaction types such as journal entries, cash transactions, and refunds.

Would you like sample VBA/Python code examples for applying these rules, or strategies for integrating them into your fraud detection workflow? ??

Question#2:

Please provide an example code in Python for a financial transaction set with amount, date in mm/dd/yy and description for

1-Irregular Time Patterns and

2-Benford’s Law and

3-threshold analysis

4-A cluster of extremely high or low transactions

5- spike in transactions on non-business days

6- A significant underrepresentation of low digits in financial entries

7-Frequent repeating digits (e.g., $11,111) or unnatural sequences (e.g., $1234, $5678) suggest manipulation.

8-Fraud Indicator: Multiple transactions slightly below an internal control threshold of $10k

9-Fraud Indicator: Identical amounts on the same date, especially with the same vendor or account number, raise suspicion.

10-Fraud Indicator: An unusually high frequency of transactions ending in ‘00’ or ‘000’ may suggest fabricated entries or manipulated rounding.

1. Python Code - Comprehensive Fraud Detection Model

This Python code will cover:

? Irregular Time Patterns ? Benford’s Law Analysis ? Threshold Analysis ? Outlier Transactions ? Weekend and Holiday Spikes ? Underrepresentation of Low Digits ? Frequent Repeating Digits ? Threshold Manipulation (e.g., just below $10,000) ? Duplicate Transactions ? Rounded Number Analysis

<<There are many powerful tools below for adapting the Py toolset to reality in finance! ??>>

Python Code Implementation

import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

from scipy.stats import chisquare

from datetime import datetime

# Sample Dataset

data = pd.DataFrame({

'Transaction_ID': range(1, 501),

'Amount': np.random.randint(1, 20000, 500), # Random financial transactions

'Date': pd.date_range(start='2023-01-01', periods=500, freq='D'),

'Description': np.random.choice(['Vendor A', 'Vendor B', 'Vendor C'], 500)

})

# Step 1: Irregular Time Patterns

data['Hour'] = np.random.choice(range(0, 24), 500)

irregular_times = data[(data['Hour'] < 6) | (data['Hour'] > 20)]

# Step 2: Benford's Law Analysis

data['Leading_Digit'] = data['Amount'].astype(str).str[0].astype(int)

benford_dist = np.log10(1 + 1 / np.arange(1, 10))

actual_dist = data['Leading_Digit'].value_counts(normalize=True).sort_index()

chi2_stat, p_value = chisquare(f_obs=actual_dist len(data), f_exp=benford_dist len(data))

# Step 3: Threshold Analysis (e.g., Transactions just below $10k)

threshold_alerts = data[(data['Amount'] > 9500) & (data['Amount'] < 10000)]

# Step 4: Outlier Analysis (Extremely High/Low Transactions)

outliers = data[(data['Amount'] > data['Amount'].quantile(0.99)) |

(data['Amount'] < data['Amount'].quantile(0.01))]

# Step 5: Spike in Weekend Transactions

data['DayOfWeek'] = data['Date'].dt.dayofweek

weekend_spikes = data[(data['DayOfWeek'] == 5) | (data['DayOfWeek'] == 6)]

# Step 6: Underrepresentation of Low Digits

low_digit_underrep = data[data['Leading_Digit'].isin([1, 2])].shape[0] / len(data)

# Step 7: Frequent Repeating Digits

repeating_digits = data[data['Amount'].astype(str).str.contains(r'(\d)\1{2,}')]

# Step 8: Threshold Manipulation

threshold_suspicious = data[(data['Amount'] > 9900) & (data['Amount'] < 10000)]

# Step 9: Duplicate Transactions

duplicate_alerts = data[data.duplicated(['Amount', 'Date', 'Description'], keep=False)]

# Step 10: Rounded Numbers

rounded_numbers = data[data['Amount'] % 100 == 0]

# Summary Output

print(f"Irregular Time Patterns Detected: {len(irregular_times)}")

print(f"Benford's Law p-value: {p_value}")

print(f"Transactions Below $10k Threshold: {len(threshold_alerts)}")

print(f"Extreme Outliers Detected: {len(outliers)}")

print(f"Weekend Spikes Detected: {len(weekend_spikes)}")

print(f"Low Digit Underrepresentation: {low_digit_underrep:.2%}")

print(f"Frequent Repeating Digits: {len(repeating_digits)}")

print(f"Suspicious Threshold Transactions: {len(threshold_suspicious)}")

print(f"Duplicate Transactions Detected: {len(duplicate_alerts)}")

print(f"Rounded Number Transactions: {len(rounded_numbers)}")

...

keywords:

#BenfordsLaw, #FraudDetection, #FinancialAudits, #python, #fraud, #finance