Loglogistic probability distribution object

A `LoglogisticDistribution`

object consists of parameters, a
model description, and sample data for a loglogistic probability
distribution.

The loglogistic distribution is closely related to the logistic distribution. If
*x* is distributed loglogistically with parameters
*μ* and *σ*, then log(*x*) is
distributed logistically with mean and standard deviation. This distribution is often
used in survival analysis to model events that experience an initial rate increase,
followed by a rate decrease.

The loglogistic distribution uses the following parameters.

Parameter | Description | Support |
---|---|---|

`mu` | Mean of logarithmic values | $$\mu >0$$ |

`sigma` | Scale parameter of logarithmic values | $$\sigma >0$$ |

There are several ways to create a `LoglogisticDistribution`

probability distribution object.

Create a distribution with specified parameter values using

`makedist`

.Fit a distribution to data using

`fitdist`

.Interactively fit a distribution to data using the

**Distribution Fitter**app.

`cdf` | Cumulative distribution function |

`icdf` | Inverse cumulative distribution function |

`iqr` | Interquartile range |

`mean` | Mean of probability distribution |

`median` | Median of probability distribution |

`negloglik` | Negative loglikelihood of probability distribution |

`paramci` | Confidence intervals for probability distribution parameters |

`pdf` | Probability density function |

`proflik` | Profile likelihood function for probability distribution |

`random` | Random numbers |

`std` | Standard deviation of probability distribution |

`truncate` | Truncate probability distribution object |

`var` | Variance of probability distribution |