1.3.6.6.6. Chi | chi square distribution pdf
1.ExploratoryDataAnalysis[1]1.3.EDATechniques[2]1.3.6.ProbabilityDistributions[3]1.3.6.6.GalleryofDistributions[4]1.3.6.6.6.Chi-SquareDistributionProbabilityDensityFunction[5]Thechi-squaredistributionresultswhenνindependentvariableswithstandardnormaldistributionsaresquaredandsummed.Theformulafortheprobabilitydensityfunctionofthechi-squaredistributionis(f(x)=frac{e{frac{-x}{2}}x{frac{u}{2}-1}}{2{frac{u}{2}}Gamma(frac{u}{2})};;;;;;;mbox{for};xge0)whereνistheshapeparameterandΓisthegammafunction...
1. Exploratory Data Analysis[1] 1.3. EDA Techniques[2] 1.3.6. Probability Distributions[3] 1.3.6.6. Gallery of Distributions[4] 1.3.6.6.6. Chi-Square Distribution Probability Density Function [5] The chi-square distribution results when ν independent variables with standard normal distributions are squared and summed. The formula for the probability density function of the chi-square distribution is( f(x) = frac{e{frac{-x} {2}}x{frac{ u} {2} - 1}} {2{frac{ u} {2}}Gamma(frac{ u} {2}) } ;;;;;;; mbox{for} ; x ge 0 )
where ν is the shape parameter and Γ is the gamma function. The formula for the gamma function is
( Gamma(a) = int_{0}{infty} {t{a-1}e{-t}dt} )
In a testing context, the chi-square distribution is treated as a "standardized distribution" (i.e., no location or scale parameters). However, in a distributional modeling context (as with other probability distributions), the chi-square distribution itself ...