Task

Write a function to verify that a given distribution of values is uniform by using the 




χ

2




{\displaystyle \chi ^{2}}

 test to see if the distribution has a likelihood of happening of at least the significance level (conventionally 5%).

The function should return a boolean that is true if the distribution is one that a uniform distribution (with appropriate number of degrees of freedom) may be expected to produce.



Reference

   an entry at the MathWorld website:   chi-squared distribution.


package require Tcl 8.5
package require math::statistics
 
proc isUniform {distribution {significance 0.05}} {
    set count [tcl::mathop::+ {*}[dict values $distribution]]
    set expected [expr {double($count) / [dict size $distribution]}]
    set X2 0.0
    foreach value [dict values $distribution] {
	set X2 [expr {$X2 + ($value - $expected)**2 / $expected}]
    }
    set degreesOfFreedom [expr {[dict size $distribution] - 1}]
    set likelihoodOfRandom [::math::statistics::incompleteGamma \
	[expr {$degreesOfFreedom / 2.0}] [expr {$X2 / 2.0}]]
    expr {$likelihoodOfRandom > $significance}
}