List of distributions by category | Vose Software

# List of distributions by category

There are many ways to classify distributions, according to use and properties. The distributions available in ModelRisk are listed, sorted by category.

### Continuous Univariate Distributions

Continuous distributions can take any number of values over a certain range for x. This range may be infinite (e.g. for the Normal distribution) in which case we speak of an unbounded distribution or finite (e.g. the Uniform distribution) in which case we speak of a bounded distribution.

The vertical scale of a relative frequency plot of an input continuous probability distribution is the probability density. It does not represent the actual probability of the corresponding x-axis value since that probability is zero. Instead, it represents the probability per x-axis unit of generating a value within a very small range around the x-axis value.

### Discrete Univariate Distributions

Discrete distributions can only take a discrete number of values. This number may be infinite (e.g. for the Poisson distribution) or finite (e.g. the Bernoulli distribution).

The vertical scale of a relative frequency plot of a discrete distribution is the actual probability of occurrence, sometimes called the probability mass. These probabilities must sum to one.

### Multivariate Distributions

Multivariate distributions describe several parameters whose values are probabilistically linked in some way. In most cases, we create the probabilistic links via one of several correlation methods. However, there are a few specific multivariate distributions that have specific, very useful purposes and are therefore worth studying more. Multivariate distributions are implemented as array functions.

### Unbounded Distributions

Unbounded distribution range from minus infinity to plus infinity. So in principle, a sampled random variable from an unbounded distribution can take any real value.

However, since the area under a distribution's curve always needs to be one, the probability of occurring for X approaches zero as X approaches plus/minus infinity.

### Left Bounded Distributions

These distributions can only take values larger than a given value (e.g. only positive values).

### Both Bounded Distributions

These are distributions that only take values within a certain (closed) interval. For example, the Beta distribution is bounded on [0,1].

### Subjective Distributions

Subjective distributions are distributions used for subjective estimating of uncertain quantities. Also see the topic about Modeling expert opinion and Eliciting distributions of expert opinion.

- Lognormal (alternative parameter) distribution

- Normal (alternative parameter) distribution

- PERT (alternative parameter) distribution

- Triangle (alternative parameter) distribution- Weibull (alternative parameter) distribution

### Risk Event Size (Severity) Distributions

These are distributions suited for modeling variables like the size or severity of insurance claims, the magnitude of a financial loss, or the size of some damage. They are often used in aggregate modeling - so these distributions are all well-suited to be used (in Object form) as parameter for aggregate modeling with ModelRisk .

### Risk event Frequency Distributions

These are distributions suited for modeling the frequency of variables like the number of insurance claims occurring, or outbreaks, lightning strikes, etc.

### Waiting Time distributions

The following distributions are commonly used for modeling waiting time, i.e. the time until some random event occurs - for example, the lifetime of a piece of equipment or system. These distributions typically are left-bounded at zero, and unbounded on the right.