Numerical applications
If
you use any of the applications in an academic or other type of work, please
refer to the relating papers in the References!
1
Bounding the probability of the union of events
1.1
Application “eventsystem1”
It generates an event system
randomly based on the pattern of Example 5.2 and 5.3 in Mádi-Nagy
(2009) and writes the probabilities of the intersections of the events up to
the given order m into the file
prob.txt. The prob.txt file is an appropriate input of Application
“bonferroni1”.
Documentation
(including the manual)
Binary
files:
eventsystem1.exe
(Windows)
eventsystem1
(Linux)
C++
source file:
References:
Mádi-Nagy, G. (2009). On Multivariate Discrete Moment
Problems: Generalization of the Bivariate Min
Algorithm for Higher Dimensions. SIAM Journal
on Optimization 19(4) 1781-1806.
click here to see the paper (.pdf)
1.2
Application “unibonferroni1”
It gives lower and upper
bounds on the probability of the union of events, based on the information of
the probability of the intersections of the events up to a certain order. The
source code can easily be rewritten to solve binomial as well as power univariate discrete moment problems.
Keywords:
probability
bounds, expectation bounds, Bonferroni-type bounds,
discrete moment problem
Documentation
(including the manual)
Binary
files:
unibonferroni1.exe
(Windows)
unibonferroni1
(Linux)
C++
source file:
References:
Prékopa, A. (1990). The discrete moment
problem and linear programming. Discrete
Applied
Mathematics, 27
235-254.
Prékopa, A. and S. Szedmák (2003). On the Numerical Solution of the Univariate Discrete Moment Problem. RUTCOR Research
Report 32-2003.
click here to see the paper (.ps)
1.3
Application “bivbonferroni1”
It gives lower and upper
bounds on the probability of the union of events, based on the information of
the probability of the intersections of the events up to a certain order. The
source code can easily be rewritten to solve binomial as well as power bivariate discrete moment problems.
Keywords:
probability
bounds, expectation bounds, bivariate Bonferroni-type bounds, discrete moment problem
Documentation
(including the manual)
Binary
files:
bivbonferroni1.exe
(Windows)
bivbonferroni1
(Linux)
C++
source file:
References:
Mádi-Nagy, G. (2005). A
method to find the best bounds in a multivariate discrete moment problem if the
basis structure is given. Studia Scientiarum Mathematicarum Hungarica, 42(2)
207-226.
click
here to see the paper (.pdf)
Mádi-Nagy, G. and A. Prékopa
(2004).On Multivariate Discrete Moment Problems and their Applications to Bounding Expectations
and Probabilities. Mathematics
of Operations Research 29(2),
pp. 229-258.
click
here to see the paper (pdf)
1.4
Application “bonferroni1”
It gives upper bound on the
probability of the union of events, based on the information of the probability
of the intersections of the events up to a certain order. The source code can
easily be rewritten to solve binomial as well as power multivariate discrete
moment problems.
Keywords:
probability
bounds, expectation bounds, multivariate Bonferroni-type
bounds, discrete moment problem
Documentation
(including the manual)
Binary
files:
bonferroni1.exe
(Windows)
bonferroni1
(Linux)
C++
source file:
References:
Mádi-Nagy, G. (2005). A
method to find the best bounds in a multivariate discrete moment problem if the
basis structure is given. Studia Scientiarum Mathematicarum Hungarica, 42(2)
207-226.
click
here to see the paper (.pdf)
Mádi-Nagy, G. (2009). On Multivariate Discrete Moment
Problems: Generalization of the Bivariate Min
Algorithm for Higher Dimensions. SIAM
Journal on Optimization 19(4)
1781-1806.
click here to see the paper (.pdf)