ZeroTruncatedGeometric {actuar} | R Documentation |

Density function, distribution function, quantile function and random
generation for the Zero-Truncated Geometric distribution with
parameter `prob`

.

dztgeom(x, prob, log = FALSE) pztgeom(q, prob, lower.tail = TRUE, log.p = FALSE) qztgeom(p, prob, lower.tail = TRUE, log.p = FALSE) rztgeom(n, prob)

`x` |
vector of (strictly positive integer) quantiles. |

`q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

`prob` |
parameter. |

`log, log.p` |
logical; if |

`lower.tail` |
logical; if |

The zero-truncated geometric distribution with `prob`

*= p*
has probability mass function

*
p(x) = p (1-p)^(x-1)*

for *x = 1, 2, …* and *0 < p < 1*, and
*p(1) = 1* when *p = 1*.
The cumulative distribution function is

*
P(x) = [F(x) - F(0)]/[1 - F(0)],*

where *F(x)* is the distribution function of the standard geometric.

The mean is *1/p* and the variance is *(1-p)/p^2*.

In the terminology of Klugman et al. (2012), the zero-truncated
geometric is a member of the *(a, b, 1)* class of
distributions with *a = 1-p* and *b = 0*.

If an element of `x`

is not integer, the result of
`dztgeom`

is zero, with a warning.

The quantile is defined as the smallest value *x* such that
*P(x) ≥ p*, where *P* is the distribution function.

`dztgeom`

gives the (log) probability mass function,
`pztgeom`

gives the (log) distribution function,
`qztgeom`

gives the quantile function, and
`rztgeom`

generates random deviates.

Invalid `prob`

will result in return value `NaN`

, with a
warning.

The length of the result is determined by `n`

for
`rztgeom`

, and is the maximum of the lengths of the
numerical arguments for the other functions.

Functions `{d,p,q}ztgeom`

use `{d,p,q}geom`

for all but
the trivial input values and *p(0)*.

`rztgeom`

uses the simple inversion algorithm suggested by
Peter Dalgaard on the r-help mailing list on 1 May 2005
(https://stat.ethz.ch/pipermail/r-help/2005-May/070680.html).

Vincent Goulet vincent.goulet@act.ulaval.ca

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012),
*Loss Models, From Data to Decisions, Fourth Edition*, Wiley.

`dgeom`

for the geometric distribution.

`dztnbinom`

for the zero-truncated negative binomial, of
which the zero-truncated geometric is a special case.

p <- 1/(1 + 0.5) dztgeom(c(1, 2, 3), prob = p) dgeom(c(1, 2, 3), p)/pgeom(0, p, lower = FALSE) # same dgeom(c(1, 2, 3) - 1, p) # same pztgeom(1, prob = 1) # point mass at 1 qztgeom(pztgeom(1:10, 0.3), 0.3)

[Package *actuar* version 3.1-4 Index]