ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Subset ▼ Power set ▼ Hyperpower set sequence ▼ Hyperpower set ▼ Hypersubset ▼ Subset algebra ▼ Subset structure ▼ Measurable space ▼ Measure space ▼ Probability space ▼ Filtered probability space ▼ Random time ▼ Stopping time ▼ Negative binomial random number ▼ Geometric random positive integer ▼ Standard exponential random positive real number ▼ Exponential random positive real number
Definition D4862
Erlang random positive real number

Let $T_1, T_2, T_3, \, \overset{d}{=} \text{Exponential}(\theta)$ each be an D214: Exponential random positive real number such that
 (i) $T_1, T_2, T_3, \, \dots$ is an D2713: Independent random collection
A D5722: Random positive real number $X \in \text{Random}(0, \infty)$ is an Erlang random positive real number with parameter $\theta$ if and only if $$X \overset{d}{=} \sum_{n = 1}^N T_n$$
Children
 ▶ D5207: Real poisson process