IRIS Toolbox Reference Manual

# Probability distribution package

This package gives quick access to basic univariate distributions. Its primary use is setting up priors in the `model/estimate` and `poster/arwm` functions.

The logdist package is called to create function handles that have several different modes of use. The primary use is to compute values that are proportional to the log of the respective density. In addition, the function handles also give you access to extra information (such as the the proper p.d.f., the name, mean, std dev, mode, and stuctural parameters of the distribution), and to a random number generator from the respective distribution.

Logdist methods:

#### Getting function handles for univariate distributions

- `chisquare` - Create function proportional to log of Chi-Squared distribution.
- `normal` - Create function proportional to log of Normal or Student distribution.
- `lognormal` - Create function proportional to log of log-normal distribution.
- `beta` - Create function proportional to log of beta distribution.
- `gamma` - Create function proportional to log of gamma distribution.
- `invgamma` - Create function proportional to log of inv-gamma distribution.
- [`t`] (logdist/t) - Create function proportional to log of Student T distribution.
- `uniform` - Create function proportional to log of uniform distribution.

#### Calling the logdist function handles

The function handles `F` created by the logdist package functions can be called the following ways:

- Get a value proportional to the log-density of the respective distribution at a particular point; this call is used within the posterior simulator:

  y = F(x)

- Get the density of the respective distribution at a particular point:

  y = F(x,'pdf')

- Get the characteristics of the distribution -- mean, std deviation, mode, and information (the inverse of the second derivative of the log density):

  m = F([],'mean') s = F([],'std') o = F([],'mode') i = F([],'info')

- Get the underlying "structural" parameters of the respective distribution:

  a = F([],'a') b = F([],'b')

- Get the name of the distribution (the names correspond to the function names, i.e. can be either of `'normal'`, `'lognormal'`, `'beta'`, `'gamma'`, `'invgamma'`, `'uniform'`):

  name = F([],'name')

- Draw a vector or matrix of random numbers from the distribution; drawing from beta, gamma, and inverse gamma requires the Statistics Toolbox:

  a = F([],'draw',1,1000);

  size(a) ans = 1 10000

#### Getting on-line help on logdist functions

    help logdist
    help logdist/function_name

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