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Represents the number of trials needed to achieve a specified number of successes: $P(X=k) = \binom{k-1}{r-1}p^r(1-p)^{k-r}$, where $p$ is the success probability and $r$ is the desired number of successes.

All outcomes are equally likely in a finite sample space: $P(X=k) = \frac{1}{n}$, where n is the number of outcomes.

Another name for the Negative Binomial Distribution when focusing on the number of unsuccessful trials before a specified number of successes occurs.

Applies Weibull distribution concepts to discrete data: $P(X=k) = q^{(k^b)} - q^{((k+1)^b)}$, where $0 < q < 1$ and $b > 0$.

Describes the probability of drawing exactly k successes from a finite population without replacement: $P(X=k) = \frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}$, where N is the population size, K is the number of successes in the population, and n is the number of draws.

Used for modeling the distribution of non-negative integers: $P(X=k) = \frac{k^{-s}}{\zeta(s)}$, where $s$ is a parameter greater than 1, and $\zeta(s)$ is the Riemann zeta function.

A distribution representing the number of successes in a sequence of n independent experiments: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $p$ is the probability of success on a single trial.

Models the number of trials until the first success: $P(X=k) = (1-p)^{k-1}p$, where $p$ is the probability of success on a single trial.

Models the number of occurrences of an event where the probabilities diminish logarithmically: $P(X=k)=-\frac{p^k}{k\ln(1-p)}$ for $k\geq 1$ and $0 < p < 1$.

Describes the frequency of items in a power-law distribution: $P(X=k) = \frac{k^{-s}}{\sum_{i=1}^{N}i^{-s}}$, where $s$ is the exponent characterizing the distribution and N is the number of elements.

Expresses the probability of a given number of events occurring in a fixed interval of time or space: $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average number of events in the interval.