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What is the detailed calculation of the Poisson distribution formula for intermittent demands?

Currently, I am testing the intermittent demand for the statistical safety stock calculation in replenishment planning, but somehow I am not getting the exact value of safety stock as per the formula below

Safety stock = 1 + k - λ

λ = Average Number of Demands per Day*Replenishment Lead Time

Average Number of Demand per Day=1/AIT (AIT represents Average Interarrival Time which can be viewed from ‘Items’ table)

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