diff -c -b -B -N stats-20040709/AndersonDarling.pm stats-20040819/AndersonDarling.pm *** stats-20040709/AndersonDarling.pm Fri Jul 9 15:31:45 2004 --- stats-20040819/AndersonDarling.pm Thu Aug 19 18:48:57 2004 *************** *** 19,26 **** # log(cdf) and log(1-cdf). # ########################################################################## ! # $Id: AndersonDarling.pm,v 1.4 2002/10/07 12:25:41 lw2j Exp $ # $Log: AndersonDarling.pm,v $ # Revision 1.4 2002/10/07 12:25:41 lw2j # Applied saner indenter script. # --- 19,29 ---- # log(cdf) and log(1-cdf). # ########################################################################## ! # $Id: AndersonDarling.pm,v 1.5 2004/08/19 17:59:50 lw2j Exp $ # $Log: AndersonDarling.pm,v $ + # Revision 1.5 2004/08/19 17:59:50 lw2j + # Tweaked it so it should auto-detect sorted data. + # # Revision 1.4 2002/10/07 12:25:41 lw2j # Applied saner indenter script. # *************** *** 46,52 **** use strict; use Symbol; - require Wrapper; require UniRand; --- 49,54 ---- *************** *** 128,133 **** --- 130,146 ---- my $n = scalar @$data_ref; my @w = (); + if (!defined($sorted_already)) { + $sorted_already = 1; + + loop: for (my $i=1; $i < $n; $i++) { + if ($data_ref->[$i] < $data_ref->[$i-1]) { + $sorted_already = 0; + last loop; + } + } + } + for (my $i=0; $i < $n; $i++) { my $w_i = &$cdf($data_ref->[$i]); *************** *** 144,150 **** # Sort the $w array, unless we're told that the data is # already in order (in which case the w_i's should also # be in order). That's increasing order, BTW. ! if ((!defined($sorted_already)) || ($sorted_already == 0)) { @w = sort { $a <=> $b } @w; } --- 157,163 ---- # Sort the $w array, unless we're told that the data is # already in order (in which case the w_i's should also # be in order). That's increasing order, BTW. ! if (!$sorted_already) { @w = sort { $a <=> $b } @w; } diff -c -b -B -N stats-20040709/KolmogorovSmirnov.pm stats-20040819/KolmogorovSmirnov.pm *** stats-20040709/KolmogorovSmirnov.pm Wed Dec 31 19:00:00 1969 --- stats-20040819/KolmogorovSmirnov.pm Thu Aug 19 18:48:57 2004 *************** *** 0 **** --- 1,433 ---- + #!/usr/local/bin/perl5 -w + # + # Purpose: + # To provide an Kolmogorov-Smirnov goodness-of-fit test. Note that + # while one can usually generate the statistic (*), in order to + # find out how significant it is, you need to consult a table + # specific to that distribution. + # + # (*) Exceptions: + # 1. It's not a continuous distribution. + # 2. You estimated the distribution from the data, in which + # case while you can compute the statistic, it's not + # valid. + # + ########################################################################## + # $Id: KolmogorovSmirnov.pm,v 1.1 2004/08/19 18:48:29 lw2j Exp $ + # $Log: KolmogorovSmirnov.pm,v $ + # Revision 1.1 2004/08/19 18:48:29 lw2j + # Initial revision + # + # + ########################################################################## + # + # Package Header + # + ########################################################################## + + package KolmogorovSmirnov; + require Exporter; + require Symbol; + + use strict; + + require Numerical; + + ########################################################################## + + BEGIN { + use Exporter (); + use Symbol; + use vars qw($VERSION @ISA @EXPORT @EXPORT_OK %EXPORT_TAGS); + + $VERSION = 1.0; + @ISA = qw(Exporter); + @EXPORT = (); + %EXPORT_TAGS = (); + @EXPORT_OK = qw( + Kolmogorov_Smirnov + + compute_probability + compute_critical + + lookup_critical + lookup_probability + ); + + return 1; + } + + + + # If you like, you can use a precomputed table that gives z values + # that go along with probabilities from 0.0001 to 1.0000 at 0.0001 + # increments. It'll load the table if you use lookup_critical or + # lookup_probability. + my $__KS_TABLE_FN = "table.Kolmogorov_Smirnov"; + my $__KS_TABLE = undef; + + + sub _load_table(); + + + + + # Given: two arguments. + # #1. Reference to the data, in the form of a univariate array. + # #2. Cumulative distribution function. + # + # Compute: + # The Kolmogorov-Smirnov test statistic. + # Specifically, the one-sided version Dn+. + # + # Returns: + # The raw K-S statistic. You still need to use a table to + # judge significance. Failure, as CDF returning undef to + # indicate an impossible value, results in undef. + # + # The data will be copied and sorted by this function, unless the + # third parameter ("sorted_already") is defined and non-zero. + sub Kolmogorov_Smirnov($$;$) { + my $data_ref = shift; + my $cdf = shift; + my $sorted_already = shift; + + defined($data_ref) || die; + defined($cdf) || die; + + (ref($data_ref) eq "ARRAY") || die; + (ref($cdf) eq "CODE") || die; + + my $n = scalar @$data_ref; + my @w = (); + + + if (!defined($sorted_already)) { + $sorted_already = 1; + + loop: for (my $i=1; $i < $n; $i++) { + if ($data_ref->[$i] < $data_ref->[$i-1]) { + $sorted_already = 0; + last loop; + } + } + } + + for (my $i=0; $i < $n; $i++) { + my $w_i = &$cdf($data_ref->[$i]); + + if (!defined($w_i)) { + return undef; + } + + $w[$i] = $w_i; + } + + # Sort the $w array, unless we're told that the data is + # already in order (in which case the w_i's should also + # be in order). That's increasing order, BTW. + if (!$sorted_already) { + @w = sort { $a <=> $b } @w; + } + + my $KS = 0; + + for (my $i=0; $i < $n; $i++) { + my $frac_expected = ($i+1)/$n; + my $cdf_val = &$cdf($w[$i]); + + if (!defined($cdf_val)) { + # Hm, impossible. + return undef; + } else { + my $D = abs($cdf_val - $frac_expected); + + if ($D > $KS) { + $KS = $D; + } + } + } + + return $KS; + } + + + + # Given a Dn value (the K-S raw statistic) and the data cardinality + # ($n), and if you like an error tolerance (absolute numbers; it's + # a convergence thang) it'll attempt to compute the probability + # that, if the data DID follow the CDF you thought it did, it would + # diverge by at least that much. + # + # If you don't give it $n, it'll assume 1. This is not really + # useful except for computing critical values. + # + # Return it, or undef on assorted failures. + sub compute_probability($$;$) { + my $Dn = shift; + my $n = (scalar(@_)) ? shift : 1; + my $errtol = (scalar(@_)) ? shift : 1e-9; + + if ((!defined($Dn)) || (!defined($n)) || ($n <= 0)) { + return undef; + } + + if ($Dn <= 0) { + return 1; + } + + my $prob = 0; + my $r = 1; + my $z = $Dn / sqrt($n); + + loop: { + my $delta = ($r % 2) ? 2 : -2; + my $e_power = -2 * ($r * $r) * ($z * $z); + + $delta *= exp($e_power); + $prob += $delta; + + if (abs($delta) >= $errtol) { + $r++; + redo loop; + } + } + + return $prob; + } + + + + # Compute critical values for a given probability. + # These values are $z values unless $n is provided, in which + # case we've already multiplied by sqrt($n). + # + # Providing $n will allow a much tighter upper bound. If + # you don't provide it and you're working with a huge $n, + # this function might fail entirely. + sub compute_critical($;$) { + my $prob = shift; + my $n = scalar(@_) ? shift : undef; + my $n_bound = defined($n) ? $n : 1e12; + + defined($prob) || die; + + if ($prob <= 0) { + # Infinite, but we can't represent it. + return undef; + } + + if ($prob >= 1) { + return 0; + } + + # Otherwise... + my $lo_thresh = 0; + my $hi_thresh = sqrt($n_bound); + + my $thresh = Numerical::inverse_search(\&compute_probability, + $prob, $lo_thresh, $hi_thresh); + + if (defined($n)) { + $thresh *= sqrt($n); + } + + return $thresh; + } + + + + # Given a probability, find the matching critical value from the table. + # It'll load the table if it hasn't done that yet. + # + # The table will eat memory and obviously doesn't give infinite + # precision, but will likely save computational time. + # + # If you give it a value of $n, it'll return the actual critical + # value (z * sqrt($n)). In most cases this won't affect correctness + # except that if you don't give it $n and ask for the critical value + # for a probability of 0. + # + # If the prob is not in the table (which would be fairly odd unless + # you have very specific tastes about probabilities), then compute + # it. + sub lookup_critical($;$n) { + my $prob = shift; + my $n = scalar(@_) ? shift : undef; + + if (!defined($prob)) { + return undef; + } + + if ($prob <= 0) { + # Infinite. Well, actually sqrt($n); the maximum $Dn value + # is no greater than $n (that's the maximum difference + # between a CDF value and the expected fraction), so the + # maximum $z <= $Dn / $n^{-1/2} is sqrt($n). + return (defined($n) ? sqrt($n) : undef); + } + + if (!defined($__KS_TABLE)) { + _load_table(); + } + + + defined($__KS_TABLE) || die; + my $table_ct = scalar (@$__KS_TABLE); + my $lo = 0; + my $hi = $table_ct - 1; + + # Binary search within table. Look for exact match. + # Well, sort of exact; this is FP math after all. + loop: { + my $mid = int(($lo+$hi)/2); + my $mid_val = $__KS_TABLE->[$mid]->[0]; + + if (abs($mid_val - $prob) <= 1e-9) { + # Should be reasonably close to equality. + + my $z = $__KS_TABLE->[$mid]->[1]; + + return (defined($n) ? ($z * sqrt($n)) : $z); + } elsif ($mid_val < $prob) { + $lo = $mid+1; + } elsif ($mid_val > $prob) { + $hi = $mid-1; + } + + if ($lo > $hi) { + last loop; + } else { + redo loop; + } + } + + # No exact match. + my $crit = compute_critical($prob, $n); + + defined($crit) || die; + return $crit; + } + + + + + # Given a deviation, it'll attempt to figure out the probability + # using the K-S table, returning the closest match. + # + # If you give it an $n value, it'll assume that the $deviation + # is a $Dn value (raw K-S statistic) and compute $z. Otherwise, + # it'll assume that the deviation is already a $z value. + # + # Unless you're incredibly lucky the deviation is probably + # not in the table... + + sub lookup_probability($;$n) { + my $deviation = shift; + my $n = scalar(@_) ? shift : undef; + my $z = (defined($n) && ($n > 0)) ? ($deviation / sqrt($n)) : + $deviation; + + if (defined($n) && ($n <= 0)) { + return undef; + } + + if (!defined($z)) { + return undef; + } + + if ($z <= 0) { + # Automatic. + return 1; + } elsif (defined($n) && ($z > sqrt($n))) { + # Impossible. + return 0; + } + + + if (!defined($__KS_TABLE)) { + _load_table(); + } + + + defined($__KS_TABLE) || die; + my $table_ct = scalar (@$__KS_TABLE); + my $lo = 0; + my $hi = $table_ct - 1; + + # Binary search within table. Look for exact match. + # Well, sort of exact; this is FP math after all. + loop: { + my $mid = int(($lo+$hi)/2); + my $mid_val = $__KS_TABLE->[$mid]->[0]; + + if (abs($mid_val - $z) <= 1e-9) { + # Should be reasonably close to equality. + + my $prob = $__KS_TABLE->[$mid]->[0]; + + return $prob; + } elsif ($mid_val < $z) { + $lo = $mid+1; + } elsif ($mid_val > $z) { + $hi = $mid; + } + + if ($lo >= $hi) { + last loop; + } else { + redo loop; + } + } + + # Logic error? + die if ($lo > $hi); + + my $prob = $__KS_TABLE->[$lo]->[0]; + return $prob; + } + + + + + + + # Load the $__KS_TABLE_FN file if it's not already loaded. + # Table is assumed to have two numbers per line, a probability + # and a z value, separated by whitespace. Lines must be in + # increasing order of probabilities. + sub _load_table() { + if (defined($__KS_TABLE)) { + return; + } + + if (!(-f ($__KS_TABLE_FN))) { + die "Cannot locate $__KS_TABLE_FN"; + } + + my $fh = gensym(); + + open($fh, $__KS_TABLE_FN) || die "Failed to open(r) '$__KS_TABLE_FN': $!"; + $__KS_TABLE = +[]; + + loop: { + my $line = <$fh>; + + if (!defined($line)) { + last loop; + } + + $line =~ s/^\s+//g; + $line =~ s/\s+$//g; + ($line =~ /\S/) || last loop; + + my @tuple = split /\s+/, $line; + + push @$__KS_TABLE, \@tuple; + redo loop; + } + + close($fh) || die "Failed to close(r) '$__KS_TABLE_FN': $!"; + } + + return 1; diff -c -b -B -N stats-20040709/README stats-20040819/README *** stats-20040709/README Fri Jul 9 15:31:45 2004 --- stats-20040819/README Thu Aug 19 18:48:57 2004 *************** *** 32,38 **** The files involved are the following: ! 14 Perl5 modules AndersonDarling.pm (Anderson-Darling goodness of fit) ArrayFoo.pm (Simple array statistics) ChiSquare.pm (Chi-square goodness of fit tester; table-based) --- 32,38 ---- The files involved are the following: ! Numerous Perl5 modules AndersonDarling.pm (Anderson-Darling goodness of fit) ArrayFoo.pm (Simple array statistics) ChiSquare.pm (Chi-square goodness of fit tester; table-based) *************** *** 42,47 **** --- 42,48 ---- 2001). Heap.pm (Basic minheap implementation) kMeans.pm (Basic k-means clustering module) + KolmogorovSmirnov.pm (Kolmogorov-Smirnov goodness-of-fit tests) mktemp.pm (Utility package for making temporary files) Numerical.pm (Simple numerical algorithms, such as a numerical function inverter. Avoid the polynomial code.) *************** *** 69,76 **** quantile_fit.pl (Identical to fit.pl, just uses GKQuantile for generating a "sample"). ! 1 data file table.chi_square (flat file that's a basic chi-square table) A simple LICENSE (essentially, do whatever you like -- open, closed -- except claim that it's yours, remove the LICENSE, --- 70,78 ---- quantile_fit.pl (Identical to fit.pl, just uses GKQuantile for generating a "sample"). ! 2 data files table.chi_square (flat file that's a basic chi-square table) + table.Kolmogorov-Smirnov (similar, but for K-S tests) A simple LICENSE (essentially, do whatever you like -- open, closed -- except claim that it's yours, remove the LICENSE, diff -c -b -B -N stats-20040709/UniRand.pm stats-20040819/UniRand.pm *** stats-20040709/UniRand.pm Fri Jul 9 15:31:45 2004 --- stats-20040819/UniRand.pm Thu Aug 19 18:48:57 2004 *************** *** 18,24 **** # # ########################################################################## ! # $Id: UniRand.pm,v 1.90 2004/04/13 14:50:13 lw2j Exp $ # $Log: UniRand.pm,v $ # Revision 1.90 2004/04/13 14:50:13 lw2j # Added termination traps to _mix_gen_ppf. --- 18,24 ---- # # ########################################################################## ! # $Id: UniRand.pm,v 1.90 2004/04/13 14:50:13 lw2j Exp Locker: lw2j $ # $Log: UniRand.pm,v $ # Revision 1.90 2004/04/13 14:50:13 lw2j # Added termination traps to _mix_gen_ppf. diff -c -b -B -N stats-20040709/table.Kolmogorov_Smirnov stats-20040819/table.Kolmogorov_Smirnov *** stats-20040709/table.Kolmogorov_Smirnov Wed Dec 31 19:00:00 1969 --- stats-20040819/table.Kolmogorov_Smirnov Thu Aug 19 18:48:57 2004 *************** *** 0 **** --- 1,10000 ---- + 0.0001 2.22563837 + 0.0002 2.14626919 + 0.0003 2.09857132 + 0.0004 2.06391625 + 0.0005 2.03624950 + 0.0006 2.01394013 + 0.0007 1.99465987 + 0.0008 1.97794251 + 0.0009 1.96285681 + 0.0010 1.94940227 + 0.0011 1.93711326 + 0.0012 1.92598943 + 0.0013 1.91556537 + 0.0014 1.90584087 + 0.0015 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