# fmddisc {GRTo}

### Description

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

### Usage

fmddisc(file, header = FALSE, colid = 1, nrep = 200, title = "fmddisc")

### Arguments

### Details

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.

### Values

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

### References

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

### Note

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

### Examples

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

Documentation reproduced from package GRTo, version 1.3. License: GPL