dWeibullCount {Countr} | R Documentation |

## 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

```
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, \dots 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. |

*Countr*version 3.5.8 Index]