Review The Important Themes Within The Sub-Questions Of Each

Review The Important Themes Within The Sub Questions Of Each Bullet Po

Review the important themes within the sub questions of each bullet point. The sub questions are designed to get you thinking about some of the important issues. Your response should provide a succinct synthesis of the key themes in a way that articulates a clear point, position, or conclusion supported by research. Select a different bullet point section than what your classmates have already posted so that we can engage several discussions on relevant topics. If all of the bullet points have been addressed, then you may begin to re-use the bullet points with the expectation that varied responses continue.

You are a manager working for an insurance company. Your job entails processing individual claims filed by policyholders. In general, few claims are expensive. Each quarter, you compile a report summarizing key claim statistics, such as the number of claims submitted, the average cost per claim, and the total cost of submitted claims. In the last quarter's report, you notice a large difference between the mean and the median claim cost, the mean cost being much higher than the median cost.

Draw a conclusion as to why you might be observing this difference in the data.

Evaluate whether this information might be useful for determining if the claims data is normally distributed.

If you conclude that the data is likely normally distributed, explain why.

If not, suggest another distribution that might best describe the data. Explain why this distribution would be a more accurate representation of the data.

Given the large difference between the two measures of central tendency, which of the two measures would you rely on in describing the average claim cost and why? Support your discussion with relevant examples, research, and rationale.

The final paragraph (three or four sentences) of your initial post should summarize the one or two key points that you are making in your initial response.

Paper For Above instruction

The noticeable discrepancy between the mean and median claim costs in the insurance claims data provides critical insight into the underlying distribution of the data. When the mean significantly exceeds the median, it typically indicates a right-skewed distribution, where a majority of claims are relatively low-cost but a small number of claims are extremely high-cost, pulling the average upward. This skewness suggests that the data are not symmetrically distributed and that the tail on the right side of the distribution is longer or fatter. Such patterns are common in insurance claims because while most claims tend to be modest, occasional catastrophic claims—such as those arising from severe accidents or natural disasters—can be disproportionately high, thus elevating the mean significantly above the median (Vaughan & Vaughan, 2018).

From a statistical perspective, this discrepancy is highly relevant in assessing whether the claim costs follow a normal distribution. The normal distribution is symmetric with the mean equal to the median, and it describes data that exhibit a bell-shaped curve. The observed difference indicates that the data are unlikely to be normally distributed because the presence of outliers or extreme values skews the data. Consequently, presuming normality could lead to inaccurate statistical inferences or budgeting errors when modeling claims data.

Instead of normal distribution, a more appropriate model might be the log-normal distribution, which naturally accommodates right-skewed data. The log-normal distribution transforms skewed data into a symmetric form after applying a logarithmic transformation, making it a better fit for claim costs where high-cost claims are rare but significantly impactful (Limpert, Stahel, & Abbt, 2001). This distribution captures the reality of insurance claim data more accurately because it reflects the multiplicative effects and variability inherent in extreme claims, allowing actuaries and analysts to better predict and manage risk.

Considering the large difference between mean and median, the median provides a more reliable measure of central tendency for describing typical claim costs. The median is less affected by outliers and skewed data, giving a more representative figure of what policyholders usually claim. Relying solely on the mean could be misleading, especially when planning reserves and setting premiums, as it might overestimate the "normal" claim cost due to the influence of outliers (Hyndman & Athanasopoulos, 2018). For example, if the mean claim cost is $5,000 but the median is $2,000, using the median would prevent over-estimating expected costs in routine scenarios, supporting more stable financial planning.

In summary, the large difference between the mean and median claim costs indicates a skewed, non-normal distribution of data, most likely right-skewed. The appropriate approach involves recognizing this skewness and opting for a distribution like the log-normal in modeling these claims. Additionally, the median offers a more accurate depiction of typical claims, aiding in more reliable decision-making. Proper understanding of these statistical measures enhances risk assessment, reserve calculation, and premium setting in insurance contexts.

References

• Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and Practice. OTexts. https://otexts.com/fpp3/
• Limpert, E., Stahel, W. A., & Abbt, M. (2001). Log-normal distributions across the sciences: Keys and clues. BioScience, 51(5), 341-352. https://doi.org/10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2
• Vaughan, E. J., & Vaughan, T. M. (2018). Fundamentals of Risk and Insurance. Wiley.
• Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2012). Loss Models: From Data to Decisions. Wiley.
• Denuit, M., Dhaene, J., & Vanduffel, S. (2005). Actuarial Theory for Dependent Risks. Wiley.
• Greenville, S. R., & Goldstein, M. (2019). Distributional modeling of insurance claim sizes: A review. Journal of Risk and Insurance, 86(2), 445–469.
• Barakat, K., & Sornette, D. (2013). Heavy tails, fat tails, and the log-normal distribution in finance: Methods for calibration. Quantitative Finance, 13(8), 1243–1257.
• Rausand, M., & Høyland, A. (2004). System Reliability Theory: Models, Statistical Methods, and Applications. Wiley.
• Taleb, N. N. (2007). The Black Swan: The Impact of the Highly Improbable. Random House.
• McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press.