Chi | chi-square distribution excel
Definition1: Thechi-squaredistributionwithkdegreesoffreedom,abbreviatedχ2(k),hasprobabilitydensityfunctionkdoesnothavetobeanintegerandcanbeanypositiverealnumber.Clickhere[1] formoretechnicaldetailsaboutthechi-squaredistribution,includingproofsofsomeofthepropositionsdescribedbelow.ExceptfortheproofofCorollary2knowledgeofcalculuswillberequired.Observation:Thechi-squaredistributionisthegammadistribution[2]whereα=k/2andβ=2.Property1:The χ2(k) distributionhasmeankandvariance2k[3]Observation:Theke...
Definition 1: The chi-square distribution with k degrees of freedom, abbreviated χ2(k), has probability density function
k does not have to be an integer and can be any positive real number.
Click here[1] for more technical details about the chi-square distribution, including proofs of some of the propositions described below. Except for the proof of Corollary 2 knowledge of calculus will be required.
Observation: The chi-square distribution is the gamma distribution[2] where α = k/2 and β = 2.
Property 1: The χ2(k) distribution has mean k and variance 2k[3]
Observation: The key statistical properties of the chi-square distribution are:
Mean = k Median ≈ k(1–2/(9k))3 Mode = max (k – 1, 0) Range = [0.∞) Variance = 2k Skewness = Kurtosis = 12/kThe following are the graphs of the pdf with degrees of freedom df = 5 and 10. As df grows larger the fat part of the curve shifts to the right and becomes more like the graph of a norma...