This class contains methods used to format results of GOF test statistics, or to apply a series of tests simultaneously and format the results. More...
static final int GNUPLOT = 0 Data file format used for plotting functions with Gnuplot.data[0...N-1], and to compare it with the uniform distribution. More...
SUSPECTP for this). More...
x on a single line, then go to the next line and calls formatp1. More...
x for a test named testName with \(p\)-value p. More...
chi2 for a test with k intervals. More...
dp, dm, d, respectively, assuming a sample of size n. More...
data with the theoretical distribution dist and formats the results. More...
Higher-level tools for applying several EDF goodness-of-fit tests simultaneously are offered here.
The environment variable activeTests specifies which tests in this list are to be performed when asking for several simultaneous tests via the functions activeTests, formatActiveTests, etc.
testType test. More...
COR) to compare the empirical distribution of \(U_{(0)},…,U_{(N-1)}\) with the uniform distribution, assuming that these sorted observations are in sortedData. More...
data, not necessarily sorted, and their empirical distribution is compared with the continuous distribution dist. More...
activeTests, and return these quantities in sVal and pVal, respectively. More...
data, not necessarily sorted, and we want to compare their empirical distribution with the distribution dist. More...
activeTests. More...
k times: Applies the GofStat.iterateSpacings transformation to the \(U_{(0)},…,U_{(N-1)}\), assuming that these observations are in sortedData, then computes the EDF test statistics and calls #activeTests(DoubleArrayList,double[],double[]) after each transformation. More...
This class contains methods used to format results of GOF test statistics, or to apply a series of tests simultaneously and format the results.
It is in fact a translation from C to Java of a set of functions that were specially written for the implementation of TestU01, a software package for testing uniform random number generators [133] .
Strictly speaking, applying several tests simultaneously makes the \(p\)-values "invalid" in the sense that the probability of having at least one \(p\)-value less than 0.01, say, is larger than 0.01. One must therefore be careful with the interpretation of these \(p\)-values (one could use, e.g., the Bonferroni inequality [118] ). Applying simultaneous tests is convenient in some situations, such as in screening experiments for detecting statistical deficiencies in random number generators. In that context, rejection of the null hypothesis typically occurs with extremely small \(p\)-values (e.g., less than \(10^{-15}\)), and the interpretation is quite obvious in this case.
The class also provides tools to plot an empirical or theoretical distribution function, by creating a data file that contains a graphic plot in a format compatible with the software specified by the environment variable graphSoft. NOTE: see also the more recent package umontreal.ssj.charts.
Note: This class uses the Colt library.
◆ activeTests() [1/2] static void activeTests ( DoubleArrayList sortedData, double [] sVal, double [] pVal ) staticComputes the EDF test statistics by calling #tests(DoubleArrayList,double[]), then computes the \(p\)-values of those that currently belong to activeTests, and return these quantities in sVal and pVal, respectively.
Assumes that \(U_{(0)},…,U_{(N-1)}\) are in sortedData and that we want to compare their empirical distribution with the uniform distribution. If \(N = 1\), only puts \(1 - {}\)sortedData.get (0) in sVal[KSP], pVal[KSP], and pVal[MEAN].
The observations are in data, not necessarily sorted, and we want to compare their empirical distribution with the distribution dist.
If \(N = 1\), only puts data.get(0) in sVal[MEAN], and \(1 - {}\)dist.cdf (data.get (0)) in sVal[KSP], pVal[KSP], and pVal[MEAN].
Formats data to plot the graph of the distribution function \(F\) over the interval \([a,b]\), and returns the result as a String.
The method dist.cdf(x) returns the value of \(F\) at \(x\). The String desc gives a short caption for the graphic plot. The method computes the \(m+1\) points \((x_i, F (x_i))\), where \(x_i = a + i (b-a)/m\) for \(i=0,1,…,m\), and formats these points into a String in a format suitable for the software specified by graphSoft. NOTE: see also the more recent class umontreal.ssj.charts.ContinuousDistChart.
Formats data to plot the graph of the density \(f(x)\) over the interval \([a,b]\), and returns the result as a String.
The method dist.density(x) returns the value of \(f(x)\) at \(x\). The String desc gives a short caption for the graphic plot. The method computes the \(m+1\) points \((x_i, f(x_i))\), where \(x_i = a + i (b-a)/m\) for \(i=0,1,…,m\), and formats these points into a String in a format suitable for the software specified by graphSoft. NOTE: see also the more recent class umontreal.ssj.charts.ContinuousDistChart.
Gets the \(p\)-values of the active EDF test statistics, which are in activeTests.
It is assumed that the values of these statistics and their \(p\)-values are already computed, in sVal and pVal, and that the sample size is n. These statistics and \(p\)-values are formated using formatp2 for each one. If n=1, prints only pVal[KSP] using formatp1.
Computes the \(p\)-value of the chi-square statistic chi2 for a test with k intervals.
Uses \(d\) decimal digits of precision in the calculations. The result of the test is returned as a string. The \(p\)-value is computed using GofStat.pDisc.
Computes the \(p\)-values of the three Kolmogorov-Smirnov statistics \(D_N^+\), \(D_N^-\), and \(D_N\), whose values are in dp, dm, d, respectively, assuming a sample of size n.
Then formats these statistics and their \(p\)-values using formatp2 for each one.
Computes the KS test statistics to compare the empirical distribution of the observations in data with the theoretical distribution dist and formats the results.
See also method kolmogorovSmirnov(double[],ContinuousDistribution,double[],double[]).
Similar to formatKS(int,double,double,double), but for the KS statistic \(D_N^+(a)\) defined in ( KSPlusJumpOne ).
Writes a header, computes the \(p\)-value and calls formatp2.
Returns the \(p\)-value \(p\) of a test, in the format "@f$1-p@f$" if \(p\) is close to 1, and \(p\) otherwise.
Uses the environment variable EPSILONP and replaces \(p\) by \(\epsilon\) when it is too small.
Returns the string "<tt>p-value of test : </tt>", then calls formatp0 to print \(p\), and adds the marker "<tt>****</tt>" if \(p\) is considered suspect (uses the environment variable SUSPECTP for this).
Returns x on a single line, then go to the next line and calls formatp1.
Formats the test statistic x for a test named testName with \(p\)-value p.
The first line of the returned string contains the name of the test and the statistic whereas the second line contains its p-value. The formated values of x and p are aligned.
Formats data to plot the empirical distribution of \(U_{(1)},…,U_{(N)}\), which are assumed to be in data[0...N-1], and to compare it with the uniform distribution.
The \(U_{(i)}\) must be sorted. The two endpoints \((0, 0)\) and \((1, 1)\) are always included in the plot. The string desc gives a short caption for the graphic plot. The data is printed in a format suitable for the software specified by graphSoft. NOTE: see also the more recent class umontreal.ssj.charts.EmpiricalChart.
Similar to iterSpacingsTests, but with the GofStat.powerRatios transformation.
true, stores all the values of the observations at each iteration graph if true, the distribution of the \(U_i\) will be plotted after each iteration f stream where the plots are written to
Repeats the following k times: Applies the GofStat.iterateSpacings transformation to the \(U_{(0)},…,U_{(N-1)}\), assuming that these observations are in sortedData, then computes the EDF test statistics and calls #activeTests(DoubleArrayList,double[],double[]) after each transformation.
The function returns the original array sortedData (the transformations are applied on a copy of sortedData). If printval = true, stores all the values into the returned String after each iteration. If graph = true, calls graphDistUnif after each iteration to print to stream f the data for plotting the distribution function of the \(U_i\).
true, stores all the values of the observations at each iteration graph if true, the distribution of the \(U_i\) will be plotted after each iteration f stream where the plots are written to
Computes all EDF test statistics enumerated above (except COR) to compare the empirical distribution of \(U_{(0)},…,U_{(N-1)}\) with the uniform distribution, assuming that these sorted observations are in sortedData.
If \(N > 1\), returns sVal with the values of the KS statistics \(D_N^+\), \(D_N^-\) and \(D_N\), of the Cramér-von Mises statistic \(W_N^2\), Watson’s \(G_N\) and \(U_N^2\), Anderson-Darling’s \(A_N^2\), and the average of the \(U_i\)’s, respectively. If \(N = 1\), only puts \(1 - {}\)sortedData.get (0) in sVal[KSP]. Calling this method is more efficient than computing these statistics separately by calling the corresponding methods in GofStat.
The observations \(V\) are in data, not necessarily sorted, and their empirical distribution is compared with the continuous distribution dist.
If \(N = 1\), only puts data.get (0) in sVal[MEAN], and \(1 - {}\)dist.cdf (data.get (0)) in sVal[KSP].
The set of EDF tests that are to be performed when calling the methods activeTests, formatActiveTests, etc.
By default, this set contains KSP, KSM, and AD. Note: MEAN and COR are always excluded from this set of active tests. The valid indices for this array are KSP, KSM, KS, AD, CM, WG, WU, MEAN, and COR.
Environment variable used in formatp0 to determine which \(p\)-values are too close to 0 or 1 to be printed explicitly.
If EPSILONP \(= \epsilon\), then any \(p\)-value less than \(\epsilon\) or larger than \(1-\epsilon\) is not written explicitly; the program simply writes "<tt>eps</tt>" or "<tt>1-eps</tt>". The default value is \(10^{-15}\).
Environment variable that selects the type of software to be used for plotting the graphs of functions.
The data files produced by #graphFunc and graphDistUnif will be in a format suitable for this selected software. The default value is GNUPLOT. To display a graphic in file f using gnuplot, for example, one can use the command "<tt>plot f with steps, x with lines</tt>" in gnuplot. graphSoft can take the values GNUPLOT or MATHEMATICA.
Environment variable used in formatp1 to determine which \(p\)-values should be marked as suspect when printing test results.
If SUSPECTP \(= \alpha\), then any \(p\)-value less than \(\alpha\) or larger than \(1-\alpha\) is considered suspect and is "singled out" by formatp1. The default value is 0.01.
= {
"KolmogorovSmirnovPlus", "KolmogorovSmirnovMinus",
"KolmogorovSmirnov", "Anderson-Darling",
"CramerVon-Mises", "Watson G", "Watson U",
"Mean", "Correlation"
}
Name of each testType test.
Could be used for printing the test results, for example.
The documentation for this class was generated from the following file:
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