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See also: Distributions introduction, Distributions in ModelRisk
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Continuous Univariate distributions
Discrete Univariate distributions
Multivariate distributions
Unbounded
distributions
Left Bounded distributions
Both Bounded distributions
Claim Size distributions
Claim Frequency distributions
Subjective distributions
Waiting Time distributions
There are many ways to classify distributions, according to use and properties. The distributions available in ModelRisk are listed, sorted by category.
See also: Continuous distributions introduction
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.
- Ascending Cumulative distribution.
- Descending Cumulative distribution.
- Extreme Value Max distribution.
- Extreme Value Min distribution.
- Fatigue Life(time) distribution.
- Generalised Logistic distribution.
- Generalized Trapezoid Uniform distribution.
- Hyperbolic-Secant distribution.
- Inverse Gaussian distribution.
- shifted Pareto distribution.
- Student, or t- distribution.
See also: Discrete distributions introduction
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.
- Discrete Uniform distribution.
- Hypergeometric distribution.
- Inverse Hypergeometric distribution.
- Negative Binomial distribution.
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.
- Multivariate Hypergeometric distribution
- Multivariate Inverse Hypergeometric distribution type1
- Multivariate Inverse Hypergeometric distribution type2
- Multivariate Normal distribution
- Negative Multinomial distribution type 1
- Negative Multinomial distribution type 2
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.
- Extreme Value Max distribution
- Extreme Value Min distribution
- Generalised logistic distribution
- Hyperbolic-Secant distribution
These distributions can only take values larger than a given value (e.g. only positive values).
- Fatigue Life(time) distribution.
- Inverse Gaussian distribution.
- Negative Binomial distribution.
- shifted Pareto distribution.
These are distributions that only take values within a certain (closed) interval. For example, the Beta distribution is bounded on [0,1].
- Ascending Cumulative distribution.
- Descending Cumulative distribution.
- Generalized Trapezoid Uniform distribution.
- Hypergeometric distribution.
- Inverse Hypergeometric distribution.
See also: Modeling expert opinion introduction
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.
- Ascending Cumulative distribution.
- Descending Cumulative distribution.
- Discrete Uniform distribution.
- Generalized Trapezoid Uniform distribution.
See also: Aggregate distributions introduction
These are distributions suited for modeling the size or severity of insurance claims. Typically they are used in aggregate modeling - so these distributions are all well-suited to be used (in Object form) as parameter for aggregate modeling with ModelRisk .
- Ascending Cumulative distribution.
- Descending Cumulative distribution.
- Extreme Value Max distribution.
- Extreme Value Min distribution.
- Generalised Logistic distribution.
- Hyperbolic-Secant distribution.
- Pareto (second type) distribution
See also: Aggregate distributions introduction
These are distributions suited for modeling the frequency of insurance claims occurring. Typically they are used in aggregate modeling - these distributions are all well-suited to be used as parameter for aggregate modeling with ModelRisk .
- Negative Binomial distribution.
The following distributions are commonly used for modeling waiting time, i.e. the time until some random event occurs. These distributions typically are left-bounded at zero, and unbounded on the right.