# Probability calculations for Weibull count models

### Description

Probability computations for the univariate Weibull count process. Several
methods are provided.
`dWeibullCount`

computes probabilities.

`dWeibullCount_loglik`

computes the log-likelihood.

`evWeibullCount`

computes the expected value and variance.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
dWeibullCount(x, shape, scale, method = c("series_acc", "series_mat",
"conv_direct", "conv_naive", "conv_dePril"), time = 1, log = FALSE,
conv_steps = 100, conv_extrap = TRUE, series_terms = 50,
series_acc_niter = 300, series_acc_eps = 1e-10)
dWeibullCount_loglik(x, shape, scale, method = c("series_acc", "series_mat",
"conv_direct", "conv_naive", "conv_dePril"), time = 1, na.rm = TRUE,
conv_steps = 100, conv_extrap = TRUE, series_terms = 50,
series_acc_niter = 300, series_acc_eps = 1e-10, weights = NULL)
evWeibullCount(xmax, shape, scale, method = c("series_acc", "series_mat",
"conv_direct", "conv_naive", "conv_dePril"), time = 1, conv_steps = 100,
conv_extrap = TRUE, series_terms = 50, series_acc_niter = 300,
series_acc_eps = 1e-10)
``` |

### Arguments

`x` |
integer (vector), the desired count values. |

`shape` |
numeric (length 1), shape parameter of the Weibull count. |

`scale` |
numeric (length 1), scale parameter of the Weibull count. |

`method` |
character, one of the available methods, see details. |

`time` |
double, length of the observation window (defaults to 1). |

`log` |
logical, if TRUE, the log of the probability will be returned. |

`conv_steps` |
numeric, number of steps used for the extrapolation. |

`conv_extrap` |
logical, should Richardson extrappolation be applied ? |

`series_terms` |
numeric, number of terms in the series expansion. |

`series_acc_niter` |
numeric, number of iterations in the Euler-van Wijngaarden algorithm. |

`series_acc_eps` |
numeric, tolerance of convergence in the Euler-van Wijngaarden algorithm. |

`na.rm` |
logical, if TRUE |

`weights` |
numeric, vector of weights to apply. If |

`xmax` |
unsigned integer, maximum count to be used. |

### Details

Argument `method`

can be used to specify the desired method, as follows:

`"series_mat"`

- series expansion using matrix techniques,

`"series_acc"`

- Euler-van Wijngaarden accelerated series expansion (default),

`"conv_direc"t`

- direct convolution method of section 2,

`"conv_naive"`

- naive convolurion described in section 3.1,

`"conv_dePril"`

- dePril convolution described in section 3.2.

The arguments have sensible default values.

### Value

for `dWeibullCount`

, a vector of probabilities
*P(x(i)), i = 1, … n*, where *n =* `length(x)`

.

for `dWeibullCount_loglik`

,
a double, the log-likelihood of the count process.

for `evWeibullCount`

, a list with components:

`ExpectedValue` |
expected value, |

`Variance` |
variance. |