Description Usage Arguments Details Value Note References See Also Examples

View source: R/ruinprob.test.R

This function provides a testing framework for the probability of ruin in the classical, compound Poisson risk process. The test can be performed using the bootstrap method or using normal approximation.

1 2 | ```
ruinprob.test(x, prob.null, type = c("bootstrap", "normal"),
nboot, bootmethod = c("nonp", "exp", "lnorm"), ...)
``` |

`x` |
a numeric vector of data values (claims) |

`prob.null` |
a number indicating the hypothesized true probability of ruin. |

`type` |
a character string determining the type of test that is performed. |

`nboot` |
a number indicating the number of bootstrap replications. |

`bootmethod` |
a character string determining how the bootstrap replications are created. |

`...` |
further arguments to be passed to |

The null hypothesis is that the probability of ruin is equal to
`prob.null`

versus the one-sided alternative that probability of ruin
is smaller than `prob.null`

.

If `type = "bootstrap"`

, a bootstrap test is performed. The arguments
`nboot`

and `bootmethod`

have to be specified. `bootmethod`

determines the kind of bootstrap: `"nonp"`

creates the usual
nonparametric bootstrap replications, while `"exp"`

and
`"lnorm"`

create parametric bootstrap replications, the former
assuming exponentially distributed claims, the latter log-normally
distributed ones.

`type = "normal"`

makes use of an asymptotic normal approximation.
The computations are a lot faster, but from a theoretical point of view
the bootstrap method is more accurate, see References.

For details about the necessary and valid arguments that might have to be
supplied for `...`

, see `ruinprob`

.

A list with class `"htest"`

containing the following components:

`statistic` |
the value of the studentized probability of ruin, i.e. the test statistic. |

`parameter` |
additional parameters. |

`p.value` |
the p-value for the test. |

`estimate` |
the estimated probability of ruin. |

`null.value` |
the specified hypothesized value of the probability of ruin. |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
a character string indicating what type of test was performed. |

`data.name` |
a character string giving the name of the data. |

Using the bootstrap method is computationally intensive. Values for
`nboot`

should not be too large, usually numbers between 50 and 200
are reasonable choices.

Baumgartner, B. and Gatto, R. (2010) *A Bootstrap Test for the
Probability of Ruin in the Compound Poisson Risk Process*. ASTIN
Bulletin, **40**(1), pp. 241–255.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
# Generating a sample of 50 exponentially distributed claims with mean 10
x <- rexp(50, 0.1)
## Not run:
# Given this sample, test whether the probability of ruin is smaller than
# 0.1 using a bootstrap test with 100 bootstrap replications.
ruinprob.test(
x = x, prob.null = 0.10, type = "bootstrap",
loading = 0.2, reserve = 100, interval = 1,
bootmethod = "nonp", nboot = 100
)
## End(Not run)
# The same test using normal approximation. This is a lot faster.
ruinprob.test(
x = x, prob.null = 0.15, type = "normal",
loading = 0.2, reserve = 100, interval = 1
)
``` |

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