List of distributions by category

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See also: Distributions introduction, Distributions in ModelRisk

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

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.

- Beta distribution

- BetaSubjective distribution

- Beta4 distribution

- Bradford distribution

- Burr distribution

- Cauchy distribution

- Chi distribution

- Chi-Squared distribution

- Ascending Cumulative distribution

- Descending Cumulative distribution

- Dagum distribution

- Erlang distribution

- Error distribution

- Error Function distribution

- Exponential distribution

- Extreme Value Max distribution

- Extreme Value Min distribution

- F distribution

- Fatigue Life(time) distribution

- Gamma distribution

- Generalized Extreme Value distribution

- Generalized Logistic distribution

- Generalized Trapezoid Uniform distribution

- Histogram distribution

- Hyperbolic-Secant distribution

- Inverse Gaussian distribution

- JohnsonB distribution

- JohnsonU distribution

- KernelCU distribution

- Kumaraswamy distribution

- Kumaraswamy4 distribution

- Laplace distribution

- Levy distribution

- Lifetime2 distribution

- Lifetime3 distribution

- LifetimeExp distribution

- LogGamma distribution

- Logistic distribution

- LogLaplace distribution

- LogLogistic distribution

- LogLogisticAlt distribution

- Lognormal distribution

- LognormalAlt distribution

- LognormalB distribution

- LognormalE distribution

- LogTriangle distribution

- LogUniform distribution

- Maxwell distribution

- Modified PERT distribution

- NCChiSq distribution

- NCF distribution

- Normal distribution

- NormalMix distribution

- Ogive distribution

- Pareto distribution

- Pareto2 distribution

- Pearson5 distribution

- Pearson6 distribution

- PERT distribution

- PERTAlt distribution

- Rayleigh distribution

- Reciprocal distribution

- Relative distribution

- Skew Normal distribution

- Slash distribution

- Split Triangle distribution

- Student, or t- distribution

- Student3 distribution

- Triangle distribution

- TriangleAlt distribution

- Uniform distribution

- Weibull distribution

- WeibullAlt distribution

- Weibull3 distribution

Discrete Univariate Distributions

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.

- Bernoulli distribution

- BetaBinomial distribution

- BetaGeometric distribution

- BetaNegBin distribution

- Binomial distribution

- Burnt Finger Poisson distribution

- Delaporte distribution

- Discrete distribution

- Discrete Fitted distribution

- Discrete Uniform distribution

- Geometric distribution

- Hypergeometric distribution

- HypergeoD

- HypergeoM

- Inverse Hypergeometric distribution

- Logarithmic distribution

- Negative Binomial distribution

- Poisson distribution

- PoissonUniform

- Polya distribution

- Skellam

- StepUniform distribution

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.

- Dirichlet distribution

- Multinomial distribution

- 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 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.

- Cauchy distribution

- Erf distribution

- Error distribution

- Extreme Value Max distribution

- Extreme Value Min distribution

- Generalised logistic distribution

- Hyperbolic-Secant distribution

- JohnsonU distribution

- Laplace distribution

- LogGamma distribution

- Logistic distribution

- Normal distribution

- Student-t distribution

Left Bounded Distributions

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

- BetaGeometric distribution

- BetaNegBin distribution

- Burr distribution

- Chi distribution

- Chi-Squared distribution

- Dagum distribution

- Delapote distribution

- Erlang distribution

- Exponential distribution

- F distribution

- Fatigue Life(time) distribution

- Gamma distribution

- Geometric distribution

- Inverse Gaussian distribution

- Levy distribution

- Logarithmic distribution

- LogGamma distribution

- LogLaplace distribution

- LogLogistic distribution

- Lognormal distribution

- LognormalB distribution

- LognormalE distribution

- NCChiSq distribution

- NCF distribution

- Negative Binomial distribution

- Pareto distribution

- Shifted Pareto distribution

- Pearson5 distribution

- Pearson6 distribution

- Poisson distribution

- Polya distribution

- Rayleigh distribution

- Weibull distribution

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].

- Bernoulli distribution

- Beta distribution

- BetaSubjective distribution

- Beta4 distribution

- BetaBinomial distribution

- Binomial distribution

- Bradford distribution

- Ascending Cumulative distribution

- Descending Cumulative distribution

- Discrete distribution

- DUniform distribution

- Generalized Trapezoid Uniform distribution

- Histogram distribution

- Hypergeometric distribution

- Inverse Hypergeometric distribution

- JohnsonB distribution

- Kumaraswamy distribution

- Kumaraswamy4 distribution

- Modified PERT distribution

- PERT distribution

- PERTAlt distribution

- Reciprocal distribution

- Relative distribution

- Split Triangle distribution

- StepUniform distribution

- Triangle distribution

- TriangleAlt distribution

- Uniform distribution

Subjective Distributions

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.

- Beta distribution

- BetaSubjective distribution

- Bradford distribution

- Ascending Cumulative distribution

- Descending Cumulative distribution

- Discrete distribution

- Discrete Uniform distribution

- Generalized Trapezoid Uniform distribution

- Histogram distribution

- JohnsonB distribution

- Kumaraswamy distribution

- Kumaraswamy4 distribution

- LogLogisticAlt distribution

- LognormalAlt distribution

- Modified PERT distribution

- PERT distribution

- PERTAlt distribution

- Reciprocal distribution

- Relative distribution

- Split Triangle distribution

- StepUniform distribution

- Triangle distribution

- TriangleAlt distribution

- Uniform distribution

- WeibullAlt distribution

Claim Size (Severity) Distributions

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 .

- Bradford distribution

- Burr distribution

- Chi distribution

- Ascending Cumulative distribution

- Descending Cumulative distribution

- Dagum distribution

- Erlang distribution

- Exponential distribution

- Extreme Value Max distribution

- Extreme Value Min distribution

- F distribution

- Fatigue Life(time) distribution

- Gamma distribution

- Generalised Logistic distribution

- Histogram distribution

- Inverse Gaussian distribution

- Hyperbolic-Secant distribution

- JohnsonB distribution.

- JohnsonU distribution

- Levy distribution

- LogGamma distribution

- Logistic distribution

- LogLaplace distribution

- LogLogistic distribution

- Lognormal distribution

- LognormalB distribution

- LognormalE distribution

- NCChiSq distribution

- NCF distribution

- Pareto distribution

- Pareto (second type) distribution

- Pearson5 distribution

- Pearson6 distribution

- Rayleigh distribution

- Relative distribution

- Weibull distribution

Claim Frequency Distributions

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 .

- BetaBinomial distribution

- BetaGeometric distribution

- BetaNegBin distribution

- Binomial distribution

- Delaporte distribution

- Geometric distribution

- Logarithmic distribution

- Negative Binomial distribution

- Poisson distribution

- Polya distribution

Waiting Time distributions

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.

- Exponential distribution

- Fatigue Life distribution

- Gamma distribution

- LogGamma distribution

- Lognormal distribution

- LognormalB distribution

- LognormalE distribution

- NCChiSq distribution

- NCF distribution

- Pareto2 distribution

- Rayleigh distribution

- Weibull distribution

Zero-Modified Counting Distributions - Equations

Zero-inflated (zeroes added)

- ZI Beta-Binomial equations

- ZI BetaGeometric equations

- ZI BetaNegBin equations

- ZI binomial distribution

- ZI Delaporte equations

- ZI geometric equations

- ZI Hypergeometric equations

- ZI inverse Hypergeometric equations

- ZI Logarithmic equations

- ZI Negative Binomial equations

- ZI Poisson equations

- ZI Polya equations

- ZI Skellam

Zero-truncated (zeroes removed)

- ZT beta-binomial equations

- ZT BetaGeometric equations

- ZT betaNegBin equations

- ZT binomial distribution

- ZT Delaporte equations

- ZT Geometric equations

- ZT Hypergeometric equations

- ZT inverse Hypergeometric equations

- ZT Negative Binomial equations

- ZT Poisson equations

- ZT Polya equations