Description Usage Arguments Details Value Note Author(s) References Examples

This function finds significant discontinuities in Frequency Magnitude Distributions (FMD).

1 |

`file` |
filename of the file to be loaded |

`header` |
whether |

`colid` |
field number for the magnitude values in |

`nrep` |
number of replicates for the bootstrap |

`title` |
main title for the plot |

This function reads magnitude values in the field which number is indicated by `colid`

in `file`

.
The function returns values of significant magnitude discontinuities (e. g. deviations from linearity) in the FMD. A bootstrap procedure is used to obtain the 90% confidence interval for magnitude
discontinuities. We assumed the distribution of the `nrep`

bootstrap replicates is not skewed. Therefore, the 90% confidence interval is simply formed by taking 5% and 95% quantiles of the bootstrap replicates as the lower and upper bound of the interval respectively. These values and the 50% quantile (median) are returned in a list by the function.
The function also returns bootstrap mean and bootstrap standard-error (standard deviation of bootstrap replicate estimates). The bootstrap margin of errors at the 90% normal confidence level is returned as the result of 1.645 \* bootstrap standard-error.
The function produces a plot showing the FMD and histograms of magnitude values for the significant
discontinuities in the FMD. The plot is stored into a file with name `file`

\_disc.png (png format file).
Values of counts in histograms are controlled by the number of replicates `nrep`

that are
used.

This function returns a list containing the following components:

`quant1 ` |
the 5%, 50% and 95% quantiles of the bootstrap replicates for the main discontinuity |

`valid ` |
the numbers of valid replicates |

`bmean ` |
the bootstrap mean values |

`bse ` |
the bootstrap standard-error values |

`bme ` |
the bootstrap margin of errors values |

`quant2 ` |
the 5%, 50% and 95% quantiles of the bootstrap replicates for the auxiliary discontinuity |

Thanks to Scott Kostyshak for telling us about the extra bootstrap package dependency. GRTo version 1.2 fixes this issue.

Daniel Amorese

D. Amorese, "Applying a change-point detection method on frequency-magnitude distributions", *Bull. seism. Soc. Am.* (2007) 97, doi:10.1785\/0120060181

1 2 | ```
fmddisc(file=system.file("extdata","IDYLLdeep.data.txt",package="GRTo"),
header=FALSE,colid=15,nrep=200,"FMD mag discontinuities")
``` |

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