Don’t forget the exponential distribution, which can represent the time of the next event in a Poisson process of a constant rate λ:
p(t;λ)=λe−λt
Or the gamma distribution, which is basically the convolution of a bunch of exponential distributions and can predict the distribution of completion times for a sequence of Poisson processes (becoming more like a normal distribution with more Poisson processes adding together):
p(t;λ,α)=λαΓ(α)xα−1e−λx
(Γ(α)=(α−1)! for positive integer values of α.)
Or the Weibull distribution, which is an extension of the exponential distribution to cases where the process slows over time (k<1, “infant mortality” if t represents time-to-failure) or accelerates over time (k>1, “aging/wear-out” if t represents time-to-failure):
p(t;λ,k)=λk(λt)k−1e−(λt)k
(Please note that all of these distributions, like the lognormal, have support on t∈[0,∞).)
Don’t forget the exponential distribution, which can represent the time of the next event in a Poisson process of a constant rate λ:
p(t;λ)=λe−λt
Or the gamma distribution, which is basically the convolution of a bunch of exponential distributions and can predict the distribution of completion times for a sequence of Poisson processes (becoming more like a normal distribution with more Poisson processes adding together):
p(t;λ,α)=λαΓ(α)xα−1e−λx
(Γ(α)=(α−1)! for positive integer values of α.)
Or the Weibull distribution, which is an extension of the exponential distribution to cases where the process slows over time (k<1, “infant mortality” if t represents time-to-failure) or accelerates over time (k>1, “aging/wear-out” if t represents time-to-failure):
p(t;λ,k)=λk(λt)k−1e−(λt)k
(Please note that all of these distributions, like the lognormal, have support on t∈[0,∞).)