Copyright (c) 1996 by Marne C. Cario and Barry L. Nelson
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HELP FILE FOR ARTAGEN
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Marne C. Cario
Updates: 2/17/96
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OVERVIEW
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The ARTAGEN software generates observations from an ARTA process
(Cario and Nelson [1]). User input consists of the ARTA marginal
distribution, the ARTA-process autocorrelations, and the AR-process
autocorrelations. Program output includes a file containing the
observations from the ARTA process and a file containing sample
statistics for the generated values. User input is read from the
file input.gen and output is written to user-specified files.
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USER INPUT
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The user must create a file called input.gen which contains the
following information in the given order.
Line 1 Name of file to which the generated observations
will be written (not to exceed 10 characters).
Line 2 Name of file to which the summary statistics
will be written (not to exceed 10 characters).
Line 3 ARTA marginal distribution (an integer from 1-11)
1 = Normal
2 = Student's t
3 = Continuous Uniform
4 = Exponential
5 = Gamma
6 = Weibull
7 = Lognormal
8 = Johnson Unbounded
9 = Johnson Bounded
10 = Empirical
11 = Discrete with Finite Support
Line 4: Number of autocorrelation lags to match (p)
(currently, not to exceed 20)
Line 5: Number of observations to generate
(currently not to exceed 20,000)
Next p lines: Lag-1 autocorrelation (a.c.) for the AR process
Lag-2 a.c. for the AR process
.
.
.
Lag-p a.c. for the AR process
For all ARTA distributions except the Normal distribution (which is
modeled as an ordinary AR process), the desired ARTA autocorrelations
appear on the next p lines. If the ARTA distribution is Normal, then
the parameters of the distribution follow the AR-process
autocorrelations.
Next p lines: Lag-1 autocorrelation (a.c.) for the ARTA process
Lag-2 a.c. for the ARTA process
.
.
.
Lag-p a.c. for the ARTA process
NOTE: The ARTA a.c.'s are just for documentation
purposes. They are not actually used
in computations.
Next lines: Parameters of the ARTA marginal distribution
All non-integer parameters are read in using
an f10.5 format (5 places before and after
the decimal). All integer parameters are read
in using an i4 format (four places, no decimal
point).
Distribution Parameters (in order)
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1 (Normal) mean
variance (must be > 0)
2 (Student's t) degrees of freedom
(must be an integer > 2)
3 (Cont. Uniform) left endpoint
right endpoint
4 (Exponential) rate parameter
(must be > 0)
5 (Gamma) scale parameter
(must be > 0)
shape parameter
(must be > 0)
6 (Weibull) scale parameter
(must be > 0)
shape parameter
(must be > 0)
7 (Lognormal) mean
variance
8 (Johnson Unb.) first shape parameter
second shape parameter
location parameter
scale parameter
(as given in Swain, Venkatraman,
and Wilson [2])
9 (Johnson Bnd.) first shape parameter
second shape parameter
location parameter
scale parameter
(as given in Swain, Venkatraman,
and Wilson [2])
10 (Empirical) number of points in cumulative
distribution function (c.d.f.)
(currently, not to exceed 2000 points)
11 (Discrete) number of points in probability
mass function
(currently, not to exceed 2000 points)
first value of mass function
probability of first value
second value of mass function
probability of second value
.
.
.
final value of mass function
probability of second value
If the ARTA marginal distribution is an empirical c.d.f., then
the user must create a file "empir.dat" containing the breakpoints of
the empirical c.d.f. ARTAGEN reads in the observations using
a free format, and does not assume that they are in ascending order.
No other user input is required.
NOTE: To avoid read errors, all input files should contain a
carriage return after the final line of input.
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PROGRAM OUTPUT
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The generated values of the ARTA process output appear in the file
specified on Line 1 of the input file. Summary statistics for the
generated values appear in the file specified on Line 2 of the
input file.
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REFERENCES
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1 Cario, M. and B.L. Nelson. 1995. Autoregressive to anything:
Time-series input processes for simulation. Operations Research
Letters, forthcoming.
2 Swain, J.J., Venkatraman, S., and J.R. Wilson. 1988. Least-squares
estimation of distribution functions in Johnson's translation
system. Journal of Statistical Computation and Simulation 29,
271-297.