# Distributions

Guesstimate supports a variety of statistical distributions beyond those selectable from confidence intervals. If the input parameters to these distribution functions are deterministic, 5000 samples will be generated at those parameter values. If the inputs are themselves sampled, one sample will be drawn, per input sample.

Distribution Name | Use Cases | Syntax |
---|---|---|

Beta (opens in a new tab) | Estimating Proporitions or Percentages | `=beta` $(\alpha, \beta)$ |

Central F (opens in a new tab) | Testing the Variance of Observed Samples | `=centralF` $(d_1, d_2)$ |

Cauchy (opens in a new tab) | The x-intercept of a ray with uniformly distributed angle | `=cauchy` $(x_0, \gamma)$ |

Chi-squared (opens in a new tab) | The sum of the squares of normal random variables | `=chisquare` $(k)$ |

Exponential (opens in a new tab) | The waiting time until the occurence of a rare event with a specified rate. | `=exponential` $(\lambda)$ |

Gamma (opens in a new tab) | A generalization of the sum of exponential random variables | `=gamma` $(k, \theta)$ |

Inverse-gamma (opens in a new tab) | The reciprocal of a gamma random variable | `=invgamma` $(\alpha, \beta)$ |

Lognormal (opens in a new tab) | The product of many positive, independent random variables | `=lognormal` $(\mu, \sigma)$ |

Normal (opens in a new tab) | The sum of many independent random variables | `=normal` $(\mu, \sigma)$ |

Student's T (opens in a new tab) | An estimator for the difference between the true mean and the mean of N independent samples of a random variable, for small N. | `=studentt` $(\nu)$ |

Weibull (opens in a new tab) | The lifetime of a component for which failure rate is proportional to time | `=weibull` $(\lambda, k)$ |

[Uniform (continuous)](https://en.wikipedia.org/wiki/Uniform_distribution_(continuous) (opens in a new tab) | An estimate where all equally sized uniforms have the same likelihood | `=uniform` $(a,b)$ |

Bernoulli (opens in a new tab) | The value 1 (success) with probability $p$, and 0 (failure) otherwise. Used for accounting for discrete trials. | `=bernoulli` $(p)$, `=test` $(p)$ |

Binomial (opens in a new tab) | The sum of $n$ independent Bernoulli distributions with parameter $p$ | `=binomial` $(n,p)$ |

Negative Binomial (opens in a new tab) | The number of success before $r$ failures is reached in a series of Bernoulli trials with parameter $p$ | `=negBinomial` $(r,p)$ |

Poisson (opens in a new tab) | The number of events occurring in a fixed interval, with known average rate $\lambda$, if events occur independently. | `=poisson` $(\lambda)$ |