Credibility Weighting Engine

python
# Limited Fluctuation Credibility (Bühlmann-Straub)
import math

def calculate_credibility_factor(exposure, expected_claims=1082, k=1000):
    """
    Calculate credibility Z based on exposure size
    
    exposure: Number of member-months
    expected_claims: Expected number of claims
    k: Full credibility standard (typically 1,000 - 1,500 claims)
    """
    # Square root rule for partial credibility
    if exposure < 12:  # Less than 1 year
        return 0.0
    
    z = math.sqrt(expected_claims / k)
    
    # Cap at 1.0 (full credibility)
    return min(z, 1.0)

def credibility_weighted_estimate(own_experience, benchmark, credibility_z):
    """
    Blend own experience with industry benchmark
    """
    weighted_estimate = (credibility_z * own_experience) + 
                        ((1 - credibility_z) * benchmark)
    
    return {
        'own_experience': own_experience,
        'benchmark': benchmark,
        'credibility_factor': credibility_z,
        'weighted_estimate': weighted_estimate,
        'own_weight_pct': credibility_z * 100,
        'benchmark_weight_pct': (1 - credibility_z) * 100
    }

# Credibility by Group Size
# (Assuming 1.2 claims PMPM avg)

# 50 lives (600 member-months/year):
#   Expected claims: 720
#   Credibility: sqrt(720/1082) = 81.5% → 0.815
#   Estimate: 81.5% own + 18.5% benchmark

# 125 lives (1,500 member-months):
#   Expected claims: 1,800
#   Credibility: sqrt(1800/1082) = 129% → capped at 1.00 (full credibility)
#   Estimate: 100% own experience

# 25 lives (300 member-months):
#   Expected claims: 360
#   Credibility: sqrt(360/1082) = 57.7% → 0.577
#   Estimate: 57.7% own + 42.3% benchmark

# Example Application:
# 75-life group (900 member-months)
#   - Own PMPM: $1,450 (one large claim spike)
#   - Industry benchmark: $950
#   - Credibility: sqrt(1080/1082) = 99.9% ≈ 1.00
#   - Weighted: (1.00 × $1,450) + (0.00 × $950) = $1,450
#
# BUT if we use Large Claim Pooling:
#   - Remove claims >$100K, recalculate
#   - Own PMPM (pooled): $875
#   - Credibility on pooled: 1.00
#   - Weighted: $875 (the volatile spike is removed)