Poisson Process Increment Probability Calculator

Calculate the probability of observing exactly k events in a time interval (s, t] for a homogeneous Poisson process

Increment Probability Calculator

Calculate P{N(t) - N(s) = k} for Poisson processes

Intensity λ (events per unit time)

The average rate of events occurring per unit time

Start Time s

End Time t

Event Count k

Number of events in the time interval (s, t]

About Increment Probabilities

P\\{N(t) - N(s) = k\\} = \\frac{[\\lambda(t-s)]^k}{k!}e^{-\\lambda(t-s)}

This follows from the Poisson distribution with parameter λ(t-s).

• Independent Increments: Events in non-overlapping intervals are independent
• Stationary Increments: Probability depends only on interval length (t-s)
• Poisson Distribution: Follows Poisson(λ(t-s)) distribution

Calculation Results

Probability of observing exactly k events in the time interval

Enter parameters and click Calculate to see results

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