F_gam_mix {ARPobservation} | R Documentation |

## Mixture of two gamma distributions and related equilibrium distribution

### Description

Random number generation from a mixture of two gamma distributions and the related equilibrium distribution,
for use with `r_behavior_stream`

.

### Usage

```
F_gam_mix(shape1, shape2, scale_ratio, mix)
```

### Arguments

`shape1` |
shape parameter for first mixture component, |

`shape2` |
shape parameter for second mixture component, |

`scale_ratio` |
ratio of first scale component to second scale component, |

`mix` |
mixing proportion of first component, |

### Value

Object of class `eq_dist`

with components `r_gen`

and `r_eq`

.

The function `r_gen(n, mean)`

generates random deviates from a mixture of two gamma distributions with specified
`mean`

, `shape1`

, `shape2`

, `scale_ratio`

, and `mix`

. The cumulative distribution function
is given by

`F(x) = p \Gamma(x; k_1, \theta_1) + (1 - p) \Gamma(x; k_2, \theta_2),`

where `\Gamma(x; k, \theta)`

is the cumulative distribution function of a Gamma random variable with shape `k`

and scale `\theta`

, and
the scale parameters are determined by the specified `mean`

and `scale_ratio`

.

The function `r_eq(n, mean)`

generates random deviates from the equilibrium distribution corresponding
to the mixture of gamma distributions.

### Examples

```
hist(F_gam_mix(2, 2, 1 / 12, 3 / 5)$r_gen(1000, 20))
hist(F_gam_mix(2, 2, 1 / 12, 3 / 5)$r_eq(1000, 20))
```

*ARPobservation*version 1.2.2 Index]