List of distributions by category

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

- Beta Subjective distribution

- Four-parameter Beta 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 Maximum distribution

- Extreme Value Minimum distribution

- F distribution

- Fatigue Life(time) distribution

- Gamma distribution

- Generalized Extreme Value distribution

- Generalized Logistic distribution

- Generalized Pareto distribution

- Generalized Trapezoid Uniform distribution

- Histogram distribution

- Hyperbolic-Secant distribution

- Inverse Gaussian distribution

- Johnson Bounded (JohnsonB) distribution

- Johnson Unbounded (JohnsonU) distribution

- Kernel Continuous Unbounded distribution

- Kumaraswamy distribution

- Four-parameter Kumaraswamy distribution

- Laplace distribution

- Levy distribution

- Lifetime (2-parameter) distribution

- Lifetime (3-parameter) distribution

- Lifetime (Exponential) distribution

- LogGamma distribution

- Logistic distribution

- LogLaplace distribution

- LogLogistic distribution

- LogLogistic (Alternative parameterization) distribution

- LogNormal distribution

- LogNormal (Alternative parameterization) distribution

- LogNormal (base B) distribution

- LogNormal (base E) distribution

- LogTriangle distribution

- LogUniform distribution

- Maxwell distribution

- Modified PERT distribution

- Non-Central Chi Squared distribution

- Non-Central F distribution

- Normal distribution

- Normal (Alternative parameterization) distribution

- Normal Mix distribution

-
Ogive distribution

- Pareto (first type) distribution

- Pareto (second type) distribution

- Pearson 5 distribution

- Pearson 6 distribution

- PERT distribution

- PERT (Alternative parameterization) distribution

- Rayleigh distribution

- Reciprocal distribution

- Relative distribution

- Skew Normal distribution

- Slash distribution

- Split Triangle distribution

- Student, or T- distribution

- Three-parameter Student distribution

- Three-Point Estimate distribution

- Triangle distribution

- Triangle (Alternative parameterization) distribution

- Uniform distribution

- Weibull distribution

- Weibull (Alternative parameterization) distribution

- Three-parameter Weibull 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

- Beta Negative Binomial distribution

- Binomial distribution

- Burnt Finger Poisson distribution

- Delaporte distribution

- Discrete distribution

- Discrete Fitted distribution

- Discrete Uniform distribution

- Geometric distribution

- Hypergeometric distribution

- Hypergeometric D distribiution

- Hypergeometric M distribution

- Inverse Hypergeometric distribution

- Logarithmic distribution

- Negative Binomial distribution

- Poisson distribution

- Poisson Uniform

- Polya distribution

- Skellam

- Step Uniform 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 Maximum distribution

- Extreme Value Minimum distribution

- Generalized logistic distribution

- Hyperbolic-Secant distribution

- Johnson Unbounded distribution

- Kernel Continuous Unbounded distribution

- Laplace distribution

- LogGamma distribution

- Logistic distribution

- Normal distribution

- Normal (alternative parameterization) distribution

- Normal Mix distribution

- Skellam distribution

- Skew Normal distribution

- Slash distribution

- Three-parameter Student distribution

- Student-t distribution

Left Bounded Distributions

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

- Beta Geometric distribution

- Beta Negative Binomial distribution

- Burnt Finger Poisson distribution

- Burr distribution

- Chi distribution

- Chi-Squared distribution

- Dagum distribution

- Delapote distribution

- Erlang distribution

- Exponential distribution

- F distribution

- Fatigue Life(time) distribution

- Gamma distribution

- Generalized Pareto distribution

- Geometric distribution

- Inverse Gaussian distribution

- Levy distribution

- Lifetime (2 parameter) distribution

- Lifetime (3 parameter) distribution

- Lifetime (Exponential) distribution

- Logarithmic distribution

- LogGamma distribution

- LogLaplace distribution

- LogLogistic distribution

- Lognormal distribution

- Lognormal (alternative paraameter) distribution

- Lognormal (base B) distribution

- Lognormal (base E) distribution

- Maxwell distribution

- Non-Central Chi Squared distribution

- Non-Central F distribution

- Negative Binomial distribution

- Pareto distribution

- Poisson Uniform distribution

- Shifted Pareto distribution

- Pearson 5 distribution

- Pearson 6 distribution

- Poisson distribution

- Polya distribution

- Rayleigh distribution

- Weibull distribution

- Weibull (alternative parameter) distribution

- Three-parameter 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

- Beta Subjective distribution

- Four-parameter Beta distribution

- Beta Binomial distribution

- Binomial distribution

- Bradford distribution

- Ascending Cumulative distribution

- Descending Cumulative distribution

- Discrete distribution

- Discrete Uniform distribution

- Generalized Trapezoid Uniform distribution

- Histogram distribution

- Hypergeometric D distribution

- Hypergeometric M distribution

- Hypergeometric distribution

- Inverse Hypergeometric distribution

- Johnson Bounded distribution

- Kumaraswamy distribution

- Four-parameter Kumaraswamy distribution

- LogTriangle distribution

- LogUniform distribution

- Modified PERT distribution

- PERT distribution

- PERT (alternative parameter) distribution

- Reciprocal distribution

- Relative distribution

- Split Triangle distribution

- Step Uniform distribution

- Three-Point Estimate distribution

- Triangle distribution

- Triangle (alternative parameter) 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

- Beta Subjective distribution

- Bradford distribution

- Ascending Cumulative distribution

- Descending Cumulative distribution

- Discrete distribution

- Discrete Uniform distribution

- Generalized Trapezoid Uniform distribution

- Histogram distribution

- Johnson Bounded distribution

- Kumaraswamy distribution

- Four-parameter Kumaraswamy distribution

- LogLogistic (alternative parameter) distribution

- Lognormal (alternative parameter) distribution

- LogTriangle distribution

- LogUniform distribution

- Modified PERT distribution

- Normal (alternative parameter) distribution

- PERT distribution

- PERT (alternative parameter) distribution

- Reciprocal distribution

- Relative distribution

- Split Triangle distribution

- Slash distribution

- Step Uniform distribution

- Three-Point Estimate distribution

- Triangle distribution

- Triangle (alternative parameter) distribution

- Uniform distribution

- Weibull (alternative parameter) distribution

Risk Event Size (Severity) Distributions

See also: Aggregate distributions introduction

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 .

- Bradford distribution

- Burr distribution

- Chi distribution

- Ascending Cumulative distribution

- Descending Cumulative distribution

- Dagum distribution

- Erlang distribution

- Exponential distribution

- Extreme Value Maximum distribution

- Extreme Value Minimum distribution

- F distribution

- Fatigue Life(time) distribution

- Gamma distribution

- Generalized Extreme Value distribution

- Generalized Logistic distribution

- Generalized Pareto distribution

- Generalized Trapezoid Uniform distribution

- Histogram distribution

- Inverse Gaussian distribution

- Hyperbolic-Secant distribution

- Johnson Bounded distribution.

- Johnson Unbounded distribution

- Levy distribution

- Lifetime (two-parameter) distribution

- Lifetime (three parameter) distribution

- Lifetime (Exponential) distribution

- LogGamma distribution

- Logistic distribution

- LogLaplace distribution

- LogLogistic distribution

- LogNormal distribution

- LogNormal (base B) distribution

- LogNormal (base E) distribution

- LogTriangle distribution

- LogUniform distribution

- Maxwell distribution

- Non-Central Chi Squared distribution

- Non-Central F distribution

- Pareto (first type) distribution

- Pareto (second type) distribution

- Pearson 5 distribution

- Pearson 6 distribution

- Rayleigh distribution

- Relative distribution

- Weibull distribution

- Three-parameter Weibull distribution

 

Risk event Frequency Distributions

See also: Aggregate distributions introduction

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

- Beta Binomial distribution

- Beta Geometric distribution

- Beta Negative Binomial distribution

- Binomial distribution

- Burnt Finger Poisson distribution

- Delaporte distribution

- Geometric distribution

- Logarithmic distribution

- Negative Binomial distribution

- Poisson distribution

- Poisson Uniform distribution

- Polya distribution

- Zero-inflated distributions

- Zero-truncated distributions

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.

- Exponential distribution

- Fatigue Life distribution

- Gamma distribution

- Generalized Pareto distribution

- Lifetime (two-parameter) distribution

- Lifetime (three parameter) distribution

- Lifetime (Exponential) distribution

- LogGamma distribution

- LogNormal distribution

- LogNormal (base B) distribution

- LogNormal (base E) distribution

- Pareto (type 2) distribution

- Rayleigh distribution

- Weibull distribution

- Three-parameter Weibull distribution

 

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