Rmetrics Updates, Changes, and Enhancements
2005-12-18 Built 221.10065
This file reports the most recent updates, changes and enhancements made
to the packages included in the Rmetrics environment. The packages are:
fBasics, fCalendar, fSeries, fMultivar, fExtremes, fOptions, fPortfolio
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Rmetrics VERSION 221.10065
2005-02-19 Rmetrics
Rmetrics has been compiled for R Version 2.2.1
2006-02-12 fCalendar
The explicit setting to timezone GMT is no longer necessary.
2006-02-12 fSeries
The long awaites GARCH functions are now available for simulating,
modelling, and forecasting GARCH and APARCH time series processes.
+++ many other smaller improvements and fixings ...
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Rmetrics VERSION 220.10064
2005-12-01 fSeries: GarchModelling
Major improvements could be achieved for the fSeries Package for GARCH
Modelling, although the GARCH modelling functions are still in an
experimental state and not yet finished.
2005-12-01 fCalendar: timeDate and timeSeries
A paper was submitted to JSS describing 'timeDate' and 'timeSeries'
Classes. A draft can be downloaded from www.rmetrics.org.
2005-12-01
Updates of the following files (if it was necessary) are now available:
CHANGES.html, COPYING.html, COPYRIGHT.html, FAQ.html, README.html
DocFactSheet.pdf, DocRefCard.pdf, DocRmetrics.pdf
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Rmetrics VERSION 220.10063
Rmetrics VERSION 211.10062
2005-11-02
This is a preliminary version with smaller modifications, updates, and
additions compared to Rmetrics 201.0061.
Not yet updated is the documentation included in DocFactSheet.pdf
Doc, DocRefcard.pdf, and DocRmetrics.pdf. These documents have Version
211.10062. This update is under progress.
The major effort was invested to make under both environments MS Windows
and Linux Rmetrics running based on the new compiler suite with
gfortran. Please note, that I have done this move for Rmetrics already
under MS Windows, although this is not yet done for R. The reason why
I have done this, is that I develop under MS Windows, and that I wan't
support two systems based on different compiler suites. The Mac Version
is not yet tested, but hopefully it will run without any problems.
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Rmetrics VERSION 201.10061
2005-07-25 fBasics: X1-BasicsData
A data set named 'usddem30u.csv' with high frequency USDDEM bid
and ask rates has been added.
2005-07-25 fBasics: B4-DistributionFits
A function named 'stableFit' for the estimation of the distributional
parameters of the stable distribution has been added.
2005-07-25 fBasics: A1-WebDataImport
A function named 'forecastsImport' for the download of time series
data from www.forecasts.org has been added.
2005-07-22 fBasics: B4-StableDistribution
A function named 'stableFit' for the estimation of the distributional
parameters of the stable distribution has been added.
2005-07-04 fMultivar: A1-BivariateTools
Density functions for the bivariate Logistic, Laplace, original
Kotz, and Exponential Power Distribution have bee added.
2005-06-19 fSeries: X3-TsayData
The data sets from Ruey Tsay's book "Analysis of Financial Time
Series" have been added.
2005-06-18 fMultivar: A0-BivariateTools
Bivariate normal and Student-t Distribution are now available
in this chapter. They are named "[dpr]norm2d" and "[dpr]t2d".
2005-06-18 fMultivar: A2-MultivariateDistribution
This chapter has been moved from "fPortfolio" to "fMultivar".
2005-06-10 fBasics: A0-BasicPlots
A grey palette named 'greyPal' has been added, like the 'rainbow'
palette for colors. Additionally internal functions .hex.to.dec
and .dec.to.hex are availalble changing number coding between
heximal and decimal number systems.
2005-06-10 fMultivar: A0-BivariateTools
A new chapter has been added with three new functions for bivariate
data modelling. The functions include a 2D grid generator, a kernel
density estimator and a histogram counter.
2005-06-06 fSeries: xmpJarqueBeraTest
Examples for the finite sample Jarque Bera Lagrange and
augmented Lagrange multiplier tests have been added.
2005-06-06 fSeries: C2-UnitrootDistribution
Functions for the computation of the probability and quantiles
for the Augmented Dickey Fuller test have been added.
2005-06-06 fBasics: C2-OneSampleTests
Functions for the finite sample Jarque Bera Lagrange and
augmented Lagrange multiplier tests have been added.
2005-06-06 fBasics: C1-TestsClass
Utility functions for plotting and interpolating finite sample
test statistics from tables have been added.
+ many other smaller improvements and fixings ...
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Rmetrics VERSION 201.10060
2005-05-12 fSeries: xmpGarchpqModelling
An example file has been added which shows step by step how to
program functions for Garch(p,q) modelling, including functions
for simulation, parameter estimation and forecasting.
2005-05-12 fSeries: A3-GarchOxModelling
Ox Interface for GARCH modelling has been updated to version
G@ARCH 4.0.
2005-05-12 fSeries: A1-ArmaModelling
A new optional argument named "rseed" added to function "armaSim".
This allows to set the random number seed.
2005-05-04 fOptions: E2-GammaFunctions
Bug in "erf" removed.
2005-05-02 fBasics: A2-BasicStatistics
The function "stdev" computes the standard deviation for a vector
or matrix and was introduced for SPlus compatibility. Under R use
the function "sd".
2005-05-02 fMultivar: B1-MatrixAddon:
A function named "pdl" has been added which returns a regressor
matrix suitable for polynomial distributed lags.
2005-05-02 fMultivar: B1-MatrixAddon:
A function named "tslag" has beeen added which returns a lagged/led
vector or matrix for given time series data.
2005-05-02 fBasics: A2-BasicStatistics
The function "basicStats" now allows also for matrix, data frame
and timeSeries inputs.
2005-04-28 fCalendar: C1-timeSeriesClass
The time Series class got a new slot named "@recordIDs". The
slot is represented by a data.frame whcih can be used for
data record identification. This may be useful for FX data
sets to name the contributor, to keep delays from the feed
or other information. For Futures this may for example name
the futures contract.
2005-04-28 fCalendar: C1-timeSeriesClass
The arguments named "colNames" have been changed to "units",
so that the naming of columns becomes unique in all 'timeSeries'
functions. Some time series functions got an additional
"units" argument.
2005-04-27 fCalendar: A1-timeDateClass
New functions for objects of class 'timeDate' have been added:
"isWeekday", "isWeekend", "isBizday", "weekDay".
2005-04-27 fCalendar: A1-timeDateClass
The ISO-8601 midnight standard has been implemented. Now
"2005-01-01 24:00:00" is a valid date/time string.
2005-04-27 fCalendar: A1-timeDateClass
A bug in the ordering of dates for unordered 'timeDate' objects
has been removed.
+ many other smaller improvements and fixings ...
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Rmetrics VERSION 201.10059
2005-04-18 released
2005-04-05 fSseries: A3-LongMemoryModeling
Nine functions have been added to estimate the self-similarity
or Hurst exponent from a long-range dependent time series process
2005-04-03 fSseries: A3-LongMemoryModeling
Three functions have been add to simulate fractional Gaussian
noise.
2005-04-03 fSseries: A3-LongMemoryModeling
Five functions have been add to simulate fractional Brownian
motion.
2005-03-25 fBasics
The basics package a been splitted into two parts. All the time, date
and calendar functions have been moved into a new package named
fCalender.
2005-03-23 fPortfolio
The portfolio package has been started. Topics about multivariate
distributions, assets modelling, drawdown statistics, value-at-risk
modelling, Markowitz portfolio, two assets portfolio and data sets
have been added.
2005-03-21 fPortfolio: A1-MultivariateDistribution
This is a collection and description of functions to compute
multivariate densities and probabilities from skew normal and
skew Student-t distribution functions. Furthermore, multivariate
random daviates can be generated, and for multivariate data,
the parameters of the underlying distribution can be estimated
by the maximum log-likelihood estimation.
2005-03-20 fPortfolio: A2-AssetsModelling
This is a collection and description of functions which generate
multivariate artficial data sets of assets, which fit the parameters
to a multivariate normal, skew normal, or (skew) Student-t distribution
and which compute some benchmark statistics. In addition a function
is provided which allows for the selection and clustering of individual
assets from portfolios using hierarchical and k-means clustering
approaches.
2005-03-19 fPortfolio: A3-DrawdownStatistics
This is a collection and description of functions which compute
drawdown statistics. Included are density, distribution function,
and random generation for the maximum drawdown distribution. In
addition the expectation of drawdowns for Brownian motion can be
computed.
2005-03-18 fPortfolio: B1-VaRModelling
This is a collection and description of functions to compute
Value-at-Risk and related risk measures for a portfolio of assets.
In addition utility functions are available to compute the maximum
loss, to calculate the total return, and to plot a histogram of
the total return.
2005-03-17 fPortfolio: B2-MarkowitzPortfolio
This is a collection and description of functions which investigate
the efficient frontier for a Markowitz portfolio from a given return
series \code{x} in the mean-variance sense when short selling is
forbidden. Tangency, equal weigths, and Monte Carlo portfolios can
also be evaluated.
2005-03-14 fPortfolio: B3-TwoAssetsPortfolio
This is a collection and description of functions which investigate
the efficient frontier for a two assets portfolio from a given return
series \code{x} in the mean-variance and CVaR sense when short selling
is forbidden.
2005-03-12 fSeries: A1-ArmaModelling
Two new functions have been added. "armaToeplitz" allows to compute
the covariance matrix from autocovariances, and "armaFischer"
computes the Fischer information matrix for an ARMA time series
process.
2005-03-03 fMultivar: X1-MultivarData
Four new data sets have been added for the examples: 'CobbDouglas' and
'logCobbDouglas' data for the Cobb-Douglas productivity function as
used in exaple 7.10 in the book of D.N. Gujarati; 'Greene4Table131'
US yearly investment data as listed in the book of W. Greene, 'pr45'
sales and durable goods data as used in the book of R.S. Pyndick and
D.L. Rubinfeld.
2005-03-02 fMultivar: B1-MatrixAddon
Functions vec and vech have been added, that stack a matrix and the
lower triangle matrix.
2005-03-02 fBasics: HyperbolicDistribution
Functions for the computation of the generalized hyperbolic distribution
have been added: dgh, pgh, qgh, and rgh.
2005-02-28 fSeries: GarchDistributions
The three chapters C2-SkewNormalDistribution, C2-SkewNormalDistribution,
C2-SkewGedDistribution have been merged to one, named C2-GarchDistributions.
C5-GarchDistributionFits has thus been renamed to C5-GarchDistributionFits.
2005-01-22 fBasics: HyperbolicDistribution
Functions to compute probability, density, quantiles and to generate
random deviates in 2nd, 3rd and 4th parameterization for the hyperbolic
distribution have been added. Furthermore, functions have been
implemented to compute the hyperbolic mode in all four parameterizations.
2005-01-21 fBasics: StableDistribution
Functions to compute probability, density, quantiles and to generate
random deviates in "S1" and "S2" parameterizations for the stable
distribution have been added. Furthermore, afunction have been
implemented to compute the stable mode.
2004-12-12 fMultivar: MatrixAddon
A function to compute the exponential of a square matrix has been
added.
2004-11-17 fSeries: fMultivar
The package 'fSeries' has become too "fat", so I partitioned it into
twp parts: 'fSeries' and 'fMultivar'. The first part now holds functions
for the analysis of time series including ARMA Modelling, GARCH
Modelling and Hypothesis Testing, the second part holds now functions
for time series anlaysis with regression methods and functions
for the technical anlaysis including rolling analysis and benchmarks.
2004-11-16 fBasics: B4-ClassicalTests/B5-StylizedFacts
The script file "B4-ClassicalTests" has become too big, so we divided
them into three new parts named "B4-TestsClass", "B5-OneSampleTests",
and "B6-TwoSampleTests". The script file "B5-StylizedFacts" has been
renamed "B7-StylizedFacts". This information is given for those who
are interested in the source code and internal structure of the Rmetrics
packages.
2004-11-14 fBasics: ClassicalTests
We made some changes on the classical test functions. We have
introduced an S4 object of class "fHTEST" which describes the
classical tests, we have added the usual arguments "title" and
"description" to the argument list, and the output of the test
now gives more information than the typical printing of R's S3
object "htest".
2004-11-13 fBasics: SPlusCompatibility
These are R functions which we made available for SPlus, including
- General Functions: strsplit, match.fun, cov, forwardsolve, %x%,
data, NROW, NCOL, sd, nlm, optim, download.file.
- Tests: bartlett.test, fligner.test, kruskal.test.
These functions may be helpful for porting Rmetrics functions
to SPlus.
2004-11-11 fSeries: garchSim
The function "garchSim" was not working properly when not all model
parameters where explicitely specified in the argument list.
Missing parameters are now added correctly. [Note, that the "garch"
functions will be replaced soon by a new completely rewritten
package in the near future.]
2004-10-29 fExtremes: gpdFit
The residual statistics and the information about threshold value
and the number of exceedances have been added to the summary report.
Now, beside numeric vectors also univariate time series objects
are accepted as input arguments.
2004-10-29 fExtremes: MdaPlots
Now, beside numeric vectors also univariate time series objects
are accepted as input arguments.
2004-10-29 fExtremes: gevFit
The residual statistics has been added to the summary report.
Now, beside numeric vectors also univariate time series objects
are accepted as input arguments.
2004-10-29 fExtremes: gevglmFit
The residual statistics has been added to the summary report.
Now, beside numeric vectors also univariate time series objects
are accepted as input arguments.
2004-10-27 fExtremes: data/*
The "bmw", "danish" and "siemens" data are now 2 column data frame
objects with the first column as ISO-8601 character dates %Y-%m-%d
and the second column as numeric values. Formerly they were numeric
vectors with POSIX date attributes. Now these data records can
easily be transformed to 'timeSeries' objects and used in the same
way as under SPlus.
2004-10-16 fOptions: xmpfOptions
Bug removed. Internal function 'readf.fOptions00Index' corrected
as '.readf.fOptions00Index'. Now the fOptions examples should work.
2004-10-16 fOptions: BesselFunctions
Modified Bessel Functions of the first and second kind for integer
order together with their derivatives have been added. The functions
are entirely written in S.
2004-10-14 fOptions: EBMDistribution
Examples have been added to the help file. In addition a bug was
fixed: An internal used variable for the computation of the second
derivative of the reciprocal Gamma and Johnson Type I distribution
was missing.
+ many other smaller improvements and fixings ...
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Rmetrics VERSION 200.10058
2004-10-11 Rmetrics
The new version is now proofed to be conform with R Version 2.0 for
all its functions.
2004-10-03 fSeries: ArmaStatistics
The functions from the "ArmaStatisticts" collection have been merged
with the collection of "ArmaModelling" functions.
2004-10-01 Rmetrics:
The naming of the source and manual page files follows now a unique
naming convention.
2004-09-27 fSeries: demo/funSeries
Three new functions have been added to the "funSeries.R" file in the
demo directory: "tslag" - computes lagged or leading vector/matrix
of selected order(s), "pdl" - creates a regressor matrix for
polynomial distributed lags, and "disaggregate" - disaggregates
a vector or time series from low to high frequency.
2004-09-21 fBasics: BasicStatistics
All column and row statistics functions now allow for 'timeSeries'
objects and any other 'rectangular' objects which can be transformed
to a matrix as input.
2004-09-19 fSeries: RollingAnalysis
All rolling anslysis functions now allow for univariate 'timeSeries'
objects and any other objects which can be transformed to a vector
as input.
2004-09-19 fSeries: TseriesTests
All test functions now allow for univariate 'timeSeries' objects and
any other objects which can be transformed to a vector as input.
2004-09-19 fBasics: DistributionFits
All fitting functions now allow for univariate 'timeSeries' objects
and any other objects which can be transformed to a vector as input.
2004-09-19 fBasics: StylizedFacts
All stylized facts functions now allow for univariate 'timeSeries'
objects and any other objects which can be transformed to a vector
as input.
2004-09-19 fBasics: ClassicalTests
All test functions now allow for univariate 'timeSeries' objects and
any other objects which can be transformed to a vector as input.
2004-09-18 fOptions: EBMDistributions, GammaFunctions, HypergeometricFunctions
Three new Chapters have been introduced with functions to compute
distributions, the error, gamma and related functions, and the
confluent hypergeometric functions. These functions are useful in the
field of Exponential Brownian Motion and for the valuation of
Asian Options. The demo file "demo/funOptions.R" where the functions
where originally listed is now obsolete.
2004-09-14 fSeries: UnitrootDistribution
Two functions to compute the cumulative probability, punitroot,
and the quantiles, qunitroot, of the unit root test statistics
have been added. The functions are based on the Fortran routine
and the tables published by J.G. McKinnon 1988.
2004-09-10 fSeries: black.ts.csv
A data file which contains real monthly stock return data from January
1978 to December 1987 which are constructed from Berndt's (1991)
data set have been added.
2004-09-10 fSeries: LongMemoryModelling
Functions to simulate the long memory behaviour of an univariate
time series process have been added. Inclided are Beran's,
Durbin's, and Paxson's method to generate Fractional Gaussian
Noise.
2004-09-08 fSeries: klein.csv
A data file which contains data for Klein's (1950) simple econometric
model of the US economy has been added.
2004-09-08 fSeries: xmpZWChapter03
Demo files with examples from Chapter 3 of the book of Zivot and
Wang "Modeling Financial Time Series with Splus" have been added.
2004-09-03 fSeries: RollingAnalysis
Caused by a typing error the function 'rollMean' failed when the
argument 'trim' was set to FALSE. This has been corrected.
2004-09-03 fSeries: EquationsModelling
We have added functions to perform fits of systems of regression
equations. The underlying functions are those from the contributed
R-package 'systemfit' written by Jeff D. Hamann and Arne Henningsen.
'systemfit' offers functions for fitting linear structural equations
using Ordinary Least Squares (OLS), Weighted Least Squares (WLS),
Seemingly Unrelated Regression (SUR), Two-Stage Least Squares (2SLS),
Weighted Two-Stage Least Squares (W2SLS) or Three-Stage Least
Squares (3SLS). The wrapper fullfills the naming conventions of
Rmetrics, returns a S4 objects, and allows for 'timeSeries' objects
as input. In addition a S-Plus like Finmetrics function 'SUR' is
made available.
2004-09-03 fSeries: xmpEqnsGreenfeld
An example to estimate Grunfeld's Model Data with OLS and SUR was
added. Different stock prices often move in the same direction at
a given point in time. The SUR technique may provide more efficient
estimates than OLS in this situation. The example was used by Zellner
in his classic. 1962 paper on seemingly unrelated regressions.
2004-09-03 fSeries: kmenta.csv
A data file which contains partly contrived data from Kmenta (1986) has
been added, constructed to illustrate estimation of a simultaneous
equation models.
2004-09-02 fBasics: HolidayCalendars
The function 'fjulian' got a new argument 'swap' making the old
one 'cc' obsolute. This change was inspired by the POSIX standard.
'swap' is an integer value which determines when dates without
the century specifications swap from the 19th to 20th century,
by default the value is 20, i.e. we swap 1920.
2004-09-02 fBasics: WebImport
A new function named 'fredImport' has been added which allows for
downloading daily financial market data from the St. Louis FED.
The import functions got a new argument 'sep' which allows to
specify the field separator in the data file, usually an Excel
*.csv file. The default is a semicolon.
2004-08-05 fSeries: DESCRIPTION
The package 'modreg' has been merged into 'stats', so we have
removed it from the dependency list in the description file.
This caused for Mac OSX operated system a failure.
2004-08-05 fSeries: surex1.ts.csv
A data file has been added which contains monthly sampled exchange
rate spot returns and forward premium data ranging from March 1976 to
June 1996 for the following currencies: USD vs. CAD, DEM, FFR, ITL,
JPY and GBP.
2004-07-07 fSeries: nelsonplosser.csv
The Nelson-Plosser data set containing the fourteen US economic time
series used by Nelson and Plosser in their seminal paper has been added.
2004-07-07 fSeries: xmpAparchModelling
The four demos "xmpAparchInnovations", "xmpAparchSimulation",
"xmpAparchEstimation", and "xmpAparchNYSERES" have been merged
to one new demo named "xmpAparchModelling" to reduce a little bit
the large number of example files.
2004-07-07 fSeries: xmpArmaModelling
The two demos "xmpArmaAnalysis", and "xmpArmaModelling", have been
merged to one new demo named "xmpArmaModelling" to reduce a little
bit the large number of example files.
2004-07-07 fBasics: xmpImportInternet
The three demos "xmpImportYahoo", "xmpImportEconomagics", and
"xmpImportForecasts" have been merged to one new demo named
"xmpImportInternet" to reduce a little bit the large number of
example files.
2004-07-07 fBasics: xmpXtsBusinessTime
The four demos "xmpXtsDailyWeeklyHists", "xmpXtsInterpolation",
"xmpXtsDeSeasonalization", and "xmpXtsDeVolatilization" have been
merged to one new demo named "xmpXtsBusinessTime" to reduce a
little bit the large number of example files.
+ many other smaller improvements and fixings ...
________________________________________________________________________________
Rmetrics VERSION 1091.10057
2004-07-04 Rmetrics
The new version is now proofed to be Debian license conform
for all its functions.
2004-07-04 FAQ
The FAQ file has been updated, now the FAQ's are providing more
information about Rmetrics.
2004-07-04 fBasics/R
In function .FirstLib we set a timezone if none found in
environment variables or options, as suggested by Dirk Eddelbuettel,
thanks Dirk.
2004-06-30 fExtremes/R
A new utility function named "gridVector" has been added which
creates all grid points from two vectors which span a rectangular
grid.
2004-06-29 fOptions/demo
A new example file named "funDensitiesEBM.R" has been added
which adds some distributions and related functions which are
useful in the theory of exponential Brownian Motion.
The functions compute densities and probabilities for the
log-Normal distribution, the Gamma distribution, the
Reciprocal-Gamma distribution, and the Johnson Type-I
distribution. Functions are made available for the compution
of moments including the Normal, the log-Normal, the
Reciprocal-Gamma, and the Asian-Option Density. In addition
a function is given to compute numerically first and second
derivatives of a given function.
2004-06-29 fOptions/demo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf", the Psis frmo
A new example file named "funSpecFunsEBM.R" has been added
with special mathematical functions which are used in the
theory of exponential Brownian Motion. The functions included
are: In Part I, the Error Function "erf