This study addresses the complex task of determining the criminal intensity posed by serial killers in a murder series by introducing the Lambda (− rate of killings) to adjust for the time span in a murder series. It focuses on examining factors related to the offender and the crime-commission process that influence victim count in a series. Methods: Generalized estimating equations with a negative binomial and a gamma log link function were used to examine factors predicting victim count in a sample of 1258 serial murder cases. Results showed that offender criminal history did not predict higher levels of Lambda when assessing victim count alone, but did predict a lower value when series length was accounted for. Killing methods were also significant predictors of a higher Lambda but were less useful when only number of victims was considered. Conclusions: Findings highlight the importance of the rate of killings along with total victim count for a more comprehensive understanding of the series' criminal intensity. This approach has implications for law enforcement and criminal profiling as it offers a more detailed perspective on the immediate threat posed by serial killers.

中文翻译：

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连环谋杀的数学：了解受害者人数和系列持续时间

本研究通过引入 Lambda（杀人率）来调整谋杀系列中的时间跨度，解决了确定连环杀手在谋杀系列中造成的犯罪强度的复杂任务。它的重点是审查与犯罪者和犯罪委员会过程有关的一系列影响受害者人数的因素。方法：使用具有负二项式和伽玛对数链接函数的广义估计方程来检查预测 1258 起连环谋杀案样本中受害者人数的因素。结果表明，仅评估受害者人数时，罪犯犯罪历史并不能预测 Lambda 水平较高，但在考虑系列长度时确实预测了较低的值。杀戮方法也是较高 Lambda 值的重要预测因素，但当仅考虑受害者数量时，作用不大。结论：调查结果强调了杀戮率和受害者总数对于更全面地了解该系列犯罪强度的重要性。这种方法对执法和犯罪侧写具有影响，因为它提供了有关连环杀手所构成的直接威胁的更详细的视角。