# Simulations

### Purpose

Enables comprehensive Monte Carlo simulations and probabilistic modeling to quantify uncertainty, evaluate risks, and simulate complex real-world scenarios across diverse domains.

### Key functions

* `CreateMetalogDistribution` — Fits a flexible "any-shape" distribution to data, capturing skewness and multimodality. 
* `CreateMetalogDistributionFromPercentiles` — Reconstructs a full probability distribution from summary statistics (e.g., P10, P50, P90). 
* `CreateSIPDataframe` — Generates a "Stochastic Information Packet" (SIP) structure, creating localized trial dataframes for lists of items to standardize Monte Carlo inputs. 
* `CreateCorrelatedSIPs` — Generates pairs of random variables with a precise Pearson correlation to preserve dependencies. 
* `CreateSLURPDistributionFromLinearRegression` — Creates SLURP distributions from linear regression models to simulate outcomes with uncertainty. 
* `CreateSLURPDistributionFromLogisticRegression` — Simulates probability distributions from logistic regression models, capturing classification uncertainty. 
* `CreateSLURPDistributionFromExponentialSmoothing` — Generates uncertainty distributions for future time-series forecasts using exponential smoothing models. 
* `SimulateNormallyDistributedOutcome` — Conducts standard Monte Carlo sampling for variables following a normal (Gaussian) distribution. 
* `SimulateTDistributedOutcome` — Simulates outcomes using a Student's T distribution, useful for small sample sizes or "fat-tailed" risks. 
* `SimulateCountOutcome` — Simulates the count of discrete events occurring in a fixed interval (Poisson distribution). 
* `SimulateCountOfSuccesses` — Simulates the number of successes in a fixed number of trials (Binomial distribution). 
* `SimulateCountUntilFirstSuccess` — Simulates the number of trials required to achieve the first success (Geometric Wait-Time). 
* `SimulateTimeBetweenEvents` — Simulates the duration between independent events occurring at a constant rate (Exponential distribution). 
* `SimulateTimeUntilNEvents` — Simulates the cumulative time required for a specific number of events to occur (Gamma distribution).

### Common use cases

* **Risk Analysis**: Quantifying the probability of extreme events, such as financial market crashes, environmental disasters, or supply chain disruptions.
* **Healthcare & Epidemiology**: Modeling disease incubation periods, recovery times, and patient flow through hospital systems under varying conditions.
* **Intelligence & Security**: Simulating signal latency, target movement patterns, and detection probabilities across multiple operational phases.
* **Project & Financial Management**: Estimating task durations, project schedule risks, and Value at Risk (VaR) for interdependent asset portfolios.