Let $N$ be a D4001: Geometric random positive integer with parameter $\theta$.
A D5216: Random natural number $M \in \mathsf{Random}(\mathbb{N})$ is a geometric random natural number if and only if \begin{equation} M \overset{d}{=} N - 1 \end{equation}

Let $X_1, X_2, X_3, \dots \in \text{Bernoulli}(\theta)$ each be a D207: Bernoulli random boolean number such that

(i)	$X_1, X_2, X_3, \dots$ is an D2713: Independent random collection
(ii)	$\theta \in (0, 1]$

A D5748: Random positive integer $G \in \text{Random} \{ 0, 1, 2, \ldots \}$ is a cogeometric random natural number with parameter $\theta$ if and only if \begin{equation} G \overset{d}{=} \max \left\{ N \in \{ 0, 1, 2, \ldots \} : \sum_{n = 1}^N X_n \neq 1 \right\} \end{equation}