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Poisson Process Event Time Calculator

Calculate probability density and distribution function for the n-th event occurrence time W_n in a Poisson process

Event Time Calculator
Calculate W_n probability density or distribution function

The average rate of events occurring per unit time

Which event occurrence time to calculate (n-th event)

Time point for calculating probability

About Event Times W_n

Mathematical Foundation:

WnsimGamma(n,lambda)W_n \\sim \\Gamma(n, \\lambda)

The n-th event time follows Gamma distribution with shape n and rate λ.

Key Properties:

  • Mean: E[Wn]=nλE[W_n] = \frac{n}{\lambda}
  • Variance: D[Wn]=nλ2D[W_n] = \frac{n}{\lambda^2}
  • Distribution: Gamma distribution Γ(n, λ)
  • Relationship: Wn=T1+T2++TnW_n = T_1 + T_2 + \cdots + T_n
Calculation Results
Results for probability density calculation

Enter parameters and click Calculate to see results