Density and random generation for the Gamma-Beta2 distribution
with shape parameters `a`

, `c`

, `d`

and rate parameter `tau`

(scale of the Beta2 distribution).

1 2 3 4 5 6 7 8 9 10 11 |

`x,q` |
vector of non-negative quantiles |

`a,c,d` |
non-negative shape parameters |

`tau` |
non-negative rate parameter |

`...` |
arguemnts passed to |

`p` |
vector of probabilities |

`n` |
number of observations to be sampled |

`k` |
the order of the moment |

`output` |
type of the |

This is the mixture distribution obtained by sampling a value *y*
from the Beta2 distribution with shape parameters *c*, *d*,
and scale *τ* and
then sampling a value from the Gamma distribution with
shape *a* and rate *y*.
The pdf involves
the Kummer confluent hypergeometric function of the second kind.
The cdf involves the generalized hypergeometric function. Its current implementation
does not work when `a-d`

is an integer, and also fails for many other cases.

`dGB2`

gives the density, `pGB2`

the cumulative function,
`rGB2`

samples from the distribution, and `summary_GB2`

gives a summary
of the distribution.

`GB2Dist`

is a generic name for the functions documented.

1 2 3 4 5 | ```
a <- 2 ; c <- 4 ; d <- 3; tau <- 1.67
sims <- rGB2(1e6, a, c, d, tau)
mean(sims); moment_GB2(1,a,c,d,tau)
mean(sims^2); moment_GB2(2,a,c,d,tau)
summary_GB2(a,c,d,tau)
``` |

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