# Named Distributions

DPL has the ability to define random variables that are drawn from named distributions, such as the normal or the beta distribution. DPL will create a discrete random variable with up to six states and calculate the probability/value pairs for those states. The approximation method DPL uses generates a discrete approximation with the same low-order moments as the original named distribution. (If n is the number of states, the approximation will match the named distribution's first 2n-1 moments.) You can see the values and probabilities DPL has calculated by looking at the computed probabilities and values in the Policy Tree.

To use named distributions, you must define a chance event that is either unconditioned or for which all conditioning events affect both probability distributions and values.

The following distributions are supported by DPL:

Beta | Geometric | Normal |

Binomial | Hyperexponential | Pascal |

Chi | Laplace | Poisson |

Chi-Square | Logistic | Rayleigh |

Erlang | Lognormal | Triangular |

Exponential | Maxwell | Uniform |

Gamma | Negative Binomial | Weibull |

It is possible for one variable to be initialized with more than one named distribution. For example, imagine a chance event C that is conditioned by a two-state chance event D. The distribution for random variable C can be a beta distribution with parameters 1.0 and 2.0 when chance event D is in state s1 and a normal distribution with parameters 2.0 and 3.0 when D is in state s2.

In some cases, you may prefer to specify certain values to be used with a named distribution and have DPL calculate the corresponding probabilities. DPL will attempt to generate appropriate probabilities. However, by constraining the algorithm you may lose accuracy, and in some cases DPL may not be able to generate a suitable distribution. If you choose to provide values, you must provide values for all states of the variable.

__Parameters__

The parameters for a named distribution may be constants or variable expressions. The parameters you will obtain in the DPL dialog may vary slightly from those defined in the mathematical equations. In particular, parameters from the Greek alphabet are converted into Roman characters.

MathematicalNotation |
DPLLanguage |

a | a |

b | b |

l, m | y |

s | sig |

*DPL Professional, DPL Enterprise, DPL Portfolio*

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