# IIDNORM.MOD

### From Support

*See also: How to read .MOD pages*

## Contents |

# Description

IIDNORM.MOD demonstrates the following functions that are related to IID (independent and identically distributed) normal random variables:

1.NOR{M,S}: Generates a normal (M,S2) pseudo random variate

2.STS{X}: Area under the standardized time series for the traced variable X

3.VAR{X}: Cumulative variance of a traced variable X

# State Variables

Variable Name | Variable Description | Size | Type |
---|---|---|---|

X | IID Pseudo-Normal variates | 1 | Real |

S | Sample Standard Deviation | 1 | Real |

STS | Area under STS function | 1 | Real |

MEAN | Mean value of iid pseudo-normal variates | 1 | Real |

STD | Standard deviation of iid pseudo-normals | 1 | Real |

# Vertices

Vertex Name | Vertex Description | State Changes |
---|---|---|

RUN | The simulation is started | Transaction termination counter for run |

GEN | Generate X | X=NOR{MEAN;STD},S=VAR{X}^.5,STS=STS{X} |

# Initialization Conditions

Variable | Description |
---|---|

MEAN | Mean value of iid pseudo-normal variates |

STD | Standard deviation of iid pseudo-normals |

# Event Relationship Graph

# English Translation

An English translation is a verbal description of a model, automatically generated by SIGMA.

The SIGMA Model, IIDNORM.MOD, is a discrete event simulation. It models Statistical functions of iid Normal Variates.

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

X: IID Pseudo-Normal variates (real valued) MEAN: Mean value of iid pseudo-normal variates (real valued) STD: Standard deviation of iid pseudo-normals (real valued) S: Sample Standard Deviation (real valued) STS: Area under STS function (real valued)

II. EVENT DEFINITIONS.

Simulation state changes are represented by event vertices (nodes or balls) in a SIGMA graph. Event vertex parameters, if any, are given in parentheses. Logical and dynamic relationships between pairs of events are represented in a SIGMA graph by edges (arrows) between event vertices. Unless otherwise stated, vertex execution priorities, to break time ties, are equal to 5.

1. The RUN(MEAN,STD) event: Initial values for, MEAN,STD, are needed for each run. After every occurrence of the RUN event: Unconditionally, schedule the GEN() event to occur in 1 time units.

2. The GEN() event: This event causes the following state change(s): X=NOR{MEAN;STD} S=VAR{X}^.5 STS=STS{X} After every occurrence of the GEN event: Unconditionally, schedule the GEN() event to occur in 1 time units.