Tcl Library Source Code

2016-08-16  Arjen Markus <[email protected]>
	* pdf_stat.tcl: Correct the use of the argument for standard deviation, affects pdf-lognormal and cdf-lognormal
	                (ticket 002b9e8e07777425)
	* statistics.test: Correct the tests for both procedures
	* statistics.tcl: Bumped the version to 1.0.1
	* pkgIndex.tcl: Load version 1.0.1 of the statistics module

2016-08-04  Arjen Markus <[email protected]>
	* interpolate.tcl: Correct the calculation of the weight for interpolation - cast to double
	* interpolate.test: Added test for this change
	* statistics.test: Correct the ANOVA tests (use -result)
	* linalg.test: Added test to show that permuted linear systems give the same result

2016-04-12  Arjen Markus <[email protected]>

    if { $stdev <= 0.0 || $mean <= 0.0 } {
	return -code error -errorcode ARG \
		-errorinfo "Standard deviation and mean must be positive" \
		"Standard deviation and mean must be positive"
    }

    set sigma [expr {sqrt(log(1.0 + $stdev*$stdev /double($mean*$mean)))}]
    set mu    [expr {log($mean) - 0.5 * $sigma * $sigma}]

    set xn   [expr {(log($x)-$mu)/$sigma}]
    set prob [expr {exp(-$xn*$xn/2.0)/$sigma/$factorNormalPdf}]

    return $prob
}

    if { $stdev <= 0.0 || $mean <= 0.0 } {
	return -code error -errorcode ARG \
		-errorinfo "Standard deviation and mean must be positive" \
		"Standard deviation and mean must be positive"
    }

    set sigma [expr {sqrt(log(1.0 + $stdev*$stdev /double($mean*$mean)))}]
    set mu    [expr {log($mean) - 0.5 * $sigma * $sigma}]

    set xn   [expr {(log($x)-$mu)/$sigma}]
    set prob1 [Cdf-toms322 1 5000 [expr {$xn*$xn}]]
    if { $xn > 0.0 } {
	set prob [expr {0.5+0.5*$prob1}]
    } else {

    if { $stdev <= 0.0 || $mean <= 0.0 } {
	return -code error -errorcode ARG \
		-errorinfo "Standard deviation and mean must be positive" \
		"Standard deviation and mean must be positive"
    }

    set sigma [expr {sqrt(log(1.0 + $stdev*$stdev /double($mean*$mean)))}]
    set mu    [expr {log($mean) - 0.5 * $sigma * $sigma}]

#    set result {}
#    for { set i 0 }  {$i < $number } { incr i } {
#        lappend result [Inverse-cdf-normal $mean $stdev [expr {rand()}]]
#    }

package ifneeded math::fourier           1.0.2 [list source [file join $dir fourier.tcl]]

if {![package vsatisfies [package provide Tcl] 8.3]} {return}
package ifneeded math::roman             1.0   [list source [file join $dir romannumerals.tcl]]

if {![package vsatisfies [package provide Tcl] 8.4]} {return}
# statistics depends on linearalgebra (for multi-variate linear regression).
package ifneeded math::statistics        1.0.1 [list source [file join $dir statistics.tcl]]
package ifneeded math::optimize          1.0.1 [list source [file join $dir optimize.tcl]]
package ifneeded math::calculus          0.8.1 [list source [file join $dir calculus.tcl]]
package ifneeded math::interpolate       1.1.1 [list source [file join $dir interpolate.tcl]]
package ifneeded math::linearalgebra     1.1.5 [list source [file join $dir linalg.tcl]]
package ifneeded math::bignum            3.1.1 [list source [file join $dir bignum.tcl]]
package ifneeded math::bigfloat          1.2.2 [list source [file join $dir bigfloat.tcl]]
package ifneeded math::machineparameters 0.1   [list source [file join $dir machineparameters.tcl]]

can be distinguished in three sets: general procedures, procedures
that deal with specific statistical distributions, list procedures to
select or transform data and simple plotting procedures (these require
Tk).

[emph Note:] The data that need to be analyzed are always contained in a
simple list. Missing values are represented as empty list elements.

[emph Note:] With version 1.0.1 a mistake in the procs [term pdf-lognormal],
[term cdf-lognormal] and [random-lognormal] has been corrected. In previous
versions the argument for the standard deviation was actually used as if
it was the variance.

[section "GENERAL PROCEDURES"]
The general statistical procedures are:

[list_begin definitions]

[call [cmd ::math::statistics::mean] [arg data]]

# version 0.6:   added pdf and cdf procedures for various distributions
#                (provided by Eric Kemp-Benedict)
# version 0.7:   added Kruskal-Wallis test (by Torsten Berg)
# version 0.8:   added Wilcoxon test and Spearman rank correlation
# version 0.9:   added kernel density estimation
# version 0.9.3: added histogram-alt, corrected test-normal
# version 1.0:   added test-anova-F
# version 1.0.1: correction in pdf-lognormal and cdf-lognormal

package require Tcl 8.4
package provide math::statistics 1.0.1
package require math

if {![llength [info commands ::lrepeat]]} {
    # Forward portability, emulate lrepeat
    proc ::lrepeat {n args} {
	if {$n < 1} {
	    return -code error "must have a count of at least 1"

        [::math::statistics::cdf-normal  0   1   1] \
        [::math::statistics::cdf-normal  0.0 1.0 1.0] \
        [::math::statistics::cdf-normal  2.0 2.0 4.0] \
        [::math::statistics::cdf-normal -2.0 2.0 0.0] \
        [::math::statistics::cdf-normal  2.0 2.0 3.0]]
} -result {0.8413205502059895 0.8413205502059895 0.8413205502059895 0.8413205502059895 0.691451459572962}

#
# The values of the mean and the standard deviation are reconstructed from mu and sigma.
# If you use mu and sigma in pdf-normal/cdf-normal, the same numbers should arise
#
test "lognormal-distribution-1.0" "Test pdf-lognormal" -match tolerant -body {
    foreach {mu sigma mean stdev} {0.0 1.0 mean1 stdev1 2.0 2.0 mean2 stdev2 -2.0 2.0 mean3 stdev3} {
        set m      [expr {exp($mu + $sigma*$sigma/2.0)}]
        set $mean  $m
        set $stdev [expr {sqrt(exp($sigma*$sigma) - 1.0) * $m}]
    }

    set x [list \
        [::math::statistics::pdf-lognormal  $mean1 $stdev1 [expr {exp(1.0)}]] \
        [::math::statistics::pdf-lognormal  $mean2 $stdev2 [expr {exp(4.0)}]] \
        [::math::statistics::pdf-lognormal  $mean3 $stdev3 [expr {exp(0.0)}]] \
        [::math::statistics::pdf-lognormal  $mean2 $stdev2 [expr {exp(3.0)}]]]
} -result {0.24197072451914337 0.12098536225957168 0.12098536225957168 0.17603266338214976}

test "lognormal-distribution-1.1" "Test cdf-lognormal" -match tolerant -body {
    foreach {mu sigma mean stdev} {0.0 1.0 mean1 stdev1 2.0 2.0 mean2 stdev2 -2.0 2.0 mean3 stdev3} {
        set m      [expr {exp($mu + $sigma*$sigma/2.0)}]
        set $mean  $m
        set $stdev [expr {sqrt(exp($sigma*$sigma) - 1.0) * $m}]
    }

    set x [list \
        [::math::statistics::cdf-lognormal  $mean1 $stdev1 [expr {exp(1.0)}]] \
        [::math::statistics::cdf-lognormal  $mean2 $stdev2 [expr {exp(4.0)}]] \
        [::math::statistics::cdf-lognormal  $mean3 $stdev3 [expr {exp(0.0)}]] \
        [::math::statistics::cdf-lognormal  $mean2 $stdev2 [expr {exp(3.0)}]]]