Overview of the program [pgraph]

This program make computations to produce the following several graphical outputs for the point process data set.
 
1. Subroutine structure of the FORTRAN program [pgraph.f].

        [pgraph]
           |-----[input]
           |-----[count1]---[shimiz]
           |-----[surviv]---[errbr2]---[plsinv]
           |         |------[unifrm]---[unitsq]
           |
           |-----[palmpr]
           |-----[vtc]
           |-----[vtcprt]

2. Cumulative numbers of events versus time, and positions of spikes (subroutine cumlat) are given in the output file [out.pgCumMT]. The R-module [r.pgCumMT] can be used to plot figures in both the console and postscript [pgCumMT.ps].

3. The output file [out.pgPTnum] gives the series of counted events in the moving interval of a fixed length. The R-module [r.pgPTnum] produces figures based on the output file [out.pgPTnum] in both the console and postscript [pgPTnum.ps]. In the figure dotted lines indicate i x (standard error), i = 1, 2, 3, assuming the stationary Poisson process ( subroutine count1 or count2 ).

4. The R-module [r.pgSurviv] produces figures based on the output files [out.pgSurviv] and [out.pgSurDev] in both the console and postscript [pgSurviv.ps]. The figures include the log survivor curve with i x (standard error), i = 1, 2, 3, based on the assumptions of the stationary Poisson process, and a similar graph in which (x, y) plots are rotated and shifted in such a way that the standard error lines and expectation lines are parallel (subroutine surviv).

5. The R-module [r.pgInterP] plots two figures based on the output files [out.pgInter1] and [out.pgInter2] in both the console and postscript [pgInterP.ps]. The first diagram is on the empirical distribution of u(i) = exp{-\mu x(i)} where x(i) is the i-th interval length between consecutive points, and \mu = (number of events) / (length of whole interval). The dashed lines of .95 and .99 significance bands of the two-sided Kolmogorov-Smirnov test assuming the uniform distribution is given. The related graph of ( u(i), u(i+1) ) plots are also carried out (subroutine uniform). 

6. The R-module [r.pgPalm] produces, in both the console and postscript [pgPalm.ps], a figure estimated intensity p(t) under the palm probability based on the output file [out.pgPalm]. The intensity p(t) is related to the covariance density c(t) by the relation of c(t) = \mu {p(t) - \mu}, where m is the mean intensity of the point process. The 0.95 and 0.99 error bands are provided assuming the stationary Poisson process (cf., subroutine palmxy, palmpr). 

7. The R-module [r.pgVTC] produces, in both the console and postscript [pgVTC.ps], a figure of the estimated variance-time curve with the 0.95 and 0.99 error lines assuming the stationary Poisson process (subroutine vtcxyp, vtcprt), based on the output file [out.pgVTC]. 

8. The input data file for this program should always be named [work.data]. Before analyzing any other data, recorded them in the same format and name the data file as [work.data]. Two example input data files [Brastings.data] and [Poisson.data] are attached in the directory of [DataExamples]. When the dataset includes remarkable clusters, one must be careful when making interpretation to the trend and cycles. 

9. The input control file [pgraph.init] gives and explains necessary variables.

10. Some example outputs are stored in the file [*.print] in the directory of [Calculations] for your initial check of the program.


This program was originally designed (January 1985) and revised (December 2005) by Yosihiko Ogata, and programmed and reprogrammed by Koichi Katsura. The R-module was designed and programmed by Jiancang Zhuang and Yosihiko Ogata (December 2005).
References

Cox, D.R. and Lewis, P.A.W. (1966) The Statistical Analysis of Series of Events, Methuen & Co. Ltd, London; also published from Chapman & Hall, London.

