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Last data update: 2014.03.03

R: Goodness-of-fit for the distribution of dates

gof.date

R Documentation

Goodness-of-fit for the distribution of dates

Description

Goodness-of-fit diagnostics for the distribution of event dates in a (assumed) Poisson process

Usage

    gof.date(date,
             start = NULL,
             end = NULL,
             plot = TRUE,
             main = NULL,
             skip = NULL,
             plot.type = "skip")

Arguments

`date`	Object of class `POSIXct` (or that can be coerced to this class) giving the dates to be tested. Must be in strictly increasing order.
`start`	The beginning of the interval, a `POSIXct` object. If `NULL`, the first event in `date` is used.
`end`	Object of class `POSIXct` the end of the interval. If `NULL`, the last event in `date` is used.
`plot`	Should a plot be shown?
`main`	Character giving the main title of the plot. The default `NULL` stands for a default main describing the period.
`skip`	Optional data.frame with columns `start` and `end` indicating start and end of skipped periods. The two columns need to be coerced to POSIXct objects. They can be POSIXct or character with POSIX datetime format.
`plot.type`	Character indicating the type of plot to produce when a `skip` data.frame is given. With `plot.type = "skip"` the plot shows missing periods as greyed rectangles and the displays the results of a Kolmogorov-Smirnov (KS) test performed on the events. For the `"omit"` case the missing periods are collapsed into vertical lines on the plot and the displayed results are for an "effective" KS test of uniformity performed omitting the missing periods.

Details

In the homogeneous Poisson process, events occur on a time interval in a uniform fashion. More precisely, for a given time interval the distribution of the event dates conditional to their number n is the distribution of the order statistics of a sample of size n of the uniform distribution on this interval.

When the interval has limits taken at events the uniformity statement remains true, but for inner events. This behaviour is met when start and end are not given and taken as the first and last events in date.

Value

A list

`effKS.statistic, KS.statistic`	Kolmogorov-Smirnov global test statistic for uniformity (bilateral test) omitting slipped periods or not.
`effKS.pvalue, KS.pavalue`	Critical probability in the KS test omitting skipped periods or not.
`effnevt, nevt`	Number of events omitting skipped periods or not.
`effduration, duration`	Effective duration i.e. total duration of non-skipped periods. In years, omitting skipped periods or not.
`effrate, rate`	Occurrence rate in number of events by year, omitting skipped periods or not.
`effduration, duation`	Total duration in years, omitting missing periods or not.
`noskip`	Data.frame object giving indications on the periods that are NOT skipped over (hence usually non-missing periods). These are : `start`, `end` (POSIX), `duration` (in years) `rate` (in number of events by year) and Kolmogorov test statistic and p-value. This data.frame is only available when a suitable `skip` has been given.

When the number of events corresponding to the indications of args is 0, the function returns NULL with a warning. When the number of events is less than 6 a warning is shown.

Warning

When skipped periods exist the number of events, duration, rate the global KS test must be computed by omitting the skipped periods in the duration and retaining only valid interevents. The indication given in nevt rate and duration should be used only when no skipped period exist (skip = NULL on input) and replaced by effnevt, effrate and effduration otherwise.

Note

In practical contexts missing periods are often met in the datasets. The diagnostic should therefore be applied on every period with no missing data. Even if the event dates seem reasonably uniform, it is a good idea to check that the rates do not differ significantly over intervals.

When some events are missing and no suitable information is given via the skip argument, the global rate, KS.statistic and KS.pvalue are of little interest. Yet the graph might be instructive.

Author(s)

Yves Deville

Examples

## Use "Brest" dataset
## simple plot. Kolmogorov-Smirnov is not useful
gof1 <- gof.date(date = Brest$OTdata$date)

## consider missing periods. Much better!
gof2 <- gof.date(date = Brest$OTdata$date,
         skip = Brest$OTmissing,
         start = Brest$OTinfo$start,
         end = Brest$OTinfo$end)

print(gof2$noskip)

## Second type of graph
gof3 <- gof.date(date = Brest$OTdata$date,
         skip = Brest$OTmissing,
         start = Brest$OTinfo$start,
         end = Brest$OTinfo$end,
         plot.type = "omit")

## non-skipped periods at Brest
ns <- skip2noskip(skip = Brest$OTmissing,
                 start = Brest$OTinfo$start,
                 end = Brest$OTinfo$end)

## say 9 plots/diagnostics
oldpar <- par(mar = c(3, 4, 3, 2), mfcol = c(3, 3))

for (i in 1:9) {
  GOF <- gof.date(date = Brest$OTdata$date,
           start = ns$start[i],
           end = ns$end[i])
}

par(oldpar)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Renext)
Loading required package: evd
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Renext/gof.date.Rd_%03d_medium.png", width=480, height=480)
> ### Name: gof.date
> ### Title: Goodness-of-fit for the distribution of dates
> ### Aliases: gof.date
> 
> ### ** Examples
> 
> ## Use "Brest" dataset
> ## simple plot. Kolmogorov-Smirnov is not useful
> gof1 <- gof.date(date = Brest$OTdata$date)
> 
> ## consider missing periods. Much better!
> gof2 <- gof.date(date = Brest$OTdata$date,
+          skip = Brest$OTmissing,
+          start = Brest$OTinfo$start,
+          end = Brest$OTinfo$end)
> 
> print(gof2$noskip)
        start        end    duration nevt      rate         Dn           KS
1  1846-01-04 1847-01-01  0.99110198   17 17.152624 0.25869353 1.717288e-01
2  1847-01-21 1852-01-21  4.99931554   48  9.601314 0.20577766 2.929104e-02
3  1852-02-08 1857-05-31  5.30869268   67 12.620810 0.19930261 8.281010e-03
4  1859-11-24 1860-01-20  0.15605749    3 19.223684 0.54385965 2.390263e-01
5  1860-05-01 1861-12-19  1.63449692   17 10.400754 0.21006996 3.869240e-01
6  1862-01-18 1863-08-31  1.61533196   15  9.286017 0.40790960 9.055002e-03
7  1864-03-01 1867-08-11  3.44421629   40 11.613672 0.13441971 4.276681e-01
8  1867-09-02 1868-07-14  0.86516085    4  4.623418 0.43670886 3.280955e-01
9  1868-08-01 1872-03-27  3.65229295   36  9.856822 0.22318008 4.680336e-02
10 1872-04-01 1872-04-14  0.03559206    0  0.000000         NA           NA
11 1872-04-20 1874-04-30  2.02600958   23 11.352365 0.31345476 1.658943e-02
12 1874-05-12 1877-08-31  3.30458590   34 10.288732 0.31068766 2.056766e-03
13 1877-10-02 1878-08-31  0.91170431   14 15.355856 0.24882025 2.991187e-01
14 1878-10-03 1891-11-02 13.08145106  118  9.020406 0.21491511 3.689848e-05
15 1891-11-30 1897-05-31  5.50034223   29  5.272399 0.18726077 2.303942e-01
16 1897-08-02 1907-05-31  9.82340862   51  5.191681 0.17492950 7.782022e-02
17 1907-07-01 1910-04-19  2.80082136   10  3.570381 0.26705767 4.022871e-01
18 1910-05-03 1911-03-22  0.88432580    7  7.915635 0.56965944 1.126370e-02
19 1911-03-29 1915-01-01  3.76180698   55 14.620633 0.13247320 2.650737e-01
20 1915-01-02 1916-12-31  1.99589322   27 13.527778 0.16735254 3.925299e-01
21 1917-02-02 1920-09-15  3.61670089   16  4.423921 0.16639856 7.073911e-01
22 1920-09-19 1922-08-31  1.94661191    9  4.623418 0.25316456 5.312227e-01
23 1922-10-02 1922-12-09  0.18617385    0  0.000000         NA           NA
24 1922-12-16 1923-07-17  0.58316222    6 10.288732 0.49530516 6.990292e-02
25 1923-07-27 1937-08-01 14.01505818  123  8.776275 0.12200363 5.137767e-02
26 1937-08-02 1937-11-01  0.24914442    2  8.027473 0.50549451 4.890714e-01
27 1939-01-01 1940-06-23  1.47570157    9  6.098794 0.38486910 1.040578e-01
28 1940-07-02 1944-04-30  3.82751540   35  9.144313 0.12511751 5.996061e-01
29 1952-09-30 1952-11-05  0.09856263    0  0.000000         NA           NA
30 1952-11-08 1952-12-22  0.12046543    1  8.301136 0.56818182 8.636364e-01
31 1952-12-25 1980-01-11 27.04449008  222  8.208696 0.05691417 4.683601e-01
32 1980-01-28 1980-02-10  0.03559206    1 28.096154 0.61538462 7.692308e-01
33 1980-02-14 1980-07-17  0.42162902    1  2.371753 0.73376623 5.324675e-01
34 1980-08-17 1981-09-20  1.09240246    3  2.746241 0.44360902 4.754802e-01
35 1981-09-29 1982-01-01  0.25735797    5 19.428191 0.79787234 6.747748e-04
36 1982-01-07 1982-05-07  0.32854209    1  3.043750 0.70000000 6.000000e-01
37 1982-05-24 1982-10-24  0.41889117    3  7.161765 0.80392157 1.507716e-02
38 1982-10-31 1982-12-06  0.09856263    1 10.145833 0.77777778 4.444444e-01
39 1982-12-20 1991-12-31  9.02943190   64  7.087932 0.10497840 4.504295e-01
40 1992-01-01 1992-12-31  0.99931554    9  9.006164 0.34581431 1.827572e-01
41 1993-01-10 1999-12-31  6.97056810   71 10.185683 0.09446467 5.200674e-01
42 2000-01-06 2008-01-10  8.01095140   92 11.484279 0.15691402 1.912773e-02
> 
> ## Second type of graph
> gof3 <- gof.date(date = Brest$OTdata$date,
+          skip = Brest$OTmissing,
+          start = Brest$OTinfo$start,
+          end = Brest$OTinfo$end,
+          plot.type = "omit")
> 
> ## non-skipped periods at Brest
> ns <- skip2noskip(skip = Brest$OTmissing,
+                  start = Brest$OTinfo$start,
+                  end = Brest$OTinfo$end)
> 
> ## say 9 plots/diagnostics
> oldpar <- par(mar = c(3, 4, 3, 2), mfcol = c(3, 3))
> 
> for (i in 1:9) {
+   GOF <- gof.date(date = Brest$OTdata$date,
+            start = ns$start[i],
+            end = ns$end[i])
+ }
Warning messages:
1: In gof.date(date = Brest$OTdata$date, start = ns$start[i], end = ns$end[i]) :
  gof.date called with a small number of evts (< 6)
2: In gof.date(date = Brest$OTdata$date, start = ns$start[i], end = ns$end[i]) :
  gof.date called with a small number of evts (< 6)
> 
> par(oldpar)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>