De indbyggede fordelingsfunktioner Chi-kvadrat (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEnJiM5Njc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU=) fordelingen hedder ChiSquare(f), hvor f angiver antallet af frihedsgrader. N\303\245r man skal arbejde med chi-kvadrat fordelingen kan man benytte de f\303\270lgende operatorer: PDF( ) (PointDistributionFunction) CDF( ) (CumulativeDistributionFunction) Quantile( ) (den inverse fordeling) Vi ser f\303\270rst p\303\245 t\303\246thedsfunktionen: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRK1N0YXRpc3RpY3NGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjpGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVkY9RkA= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder 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 Det kan godt se lidt uoverskueligt ud p\303\245 grund af Gammafunktionen, men for konkrete v\303\246rdier af frihedsgraden forenkles udtrykket - ikke mindst for de lige frihedsgrader: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder 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 Det er ogs\303\245 nemt at afbilde t\303\246thedsfunktionen (som har maksimum i x = f - 2, dvs. i dette tilf\303\246lde x = 3): 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; 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# input placeholder 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 Igen ser det lidt uoverskueligt ud, og igen forenkles udtrykket for konkrete v\303\246rdier af frihedsgraden, is\303\246r for de lige v\303\246rdier: 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEifGZyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkQtSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYnLUkkbXRkR0YkNigtSSNtbkdGJDYkUSIwRidGLy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGVi8lK2dyb3VwYWxpZ25HRlYvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGZ24tRk42KC1GIzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR0Y0L0YwUSdpdGFsaWNGJy1GLDYtUSI8RidGLy9GM0Y3RjUvRjlGN0Y6RjxGPkZAL0ZDUSwwLjI3Nzc3NzhlbUYnL0ZGRlxwRlAvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjdGL0ZURldGWUZlbkZobkZURldGWS1GSzYnLUZONigtRiM2Ji1GUTYkRmduRi8tRiw2LVEoJm1pbnVzO0YnRi9GaW9GNUZqb0Y6RjxGPkZAL0ZDUSwwLjIyMjIyMjJlbUYnL0ZGRl9xLUYjNiYtSSVtc3VwR0YkNiUtRiw2LVEvJkV4cG9uZW50aWFsRTtGJ0YvRmlvRjVGam9GOkY8Rj5GQC9GQ1EmMC4wZW1GJy9GRlEsMC4xMTExMTExZW1GJy1GIzYnLUYsNi1RKiZ1bWludXMwO0YnRi9GaW9GNUZqb0Y6RjxGPkZARl5xRmBxLUYjNigtSSZtZnJhY0dGJDYoRmlwLUZRNiRRIjJGJ0YvLyUubGluZXRoaWNrbmVzc0dGZ24vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXnMvJSliZXZlbGxlZEdGNy1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0Zpb0Y1RmpvRjpGPEY+RkBGaXEvRkZGanEtRiM2JEZeb0YvRl5wRmFwRi9GXnBGYXBGLy8lMXN1cGVyc2NyaXB0c2hpZnRHRlNGY3MtSShtZmVuY2VkR0YkNiQtRiM2JkZpcC1GLDYtUSIrRidGL0Zpb0Y1RmpvRjpGPEY+RkBGXnFGYHFGYnJGL0YvRi9GL0ZURldGWUZlbkZobi1GTjYoLUZfbzYlUSpvdGhlcndpc2VGJ0Zib0Zkb0ZURldGWUZlbkZobkZURldGWS8lJmFsaWduR1ElYXhpc0YnL0ZVUSliYXNlbGluZUYnL0ZYRl5zL0ZaUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGNC8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmR1LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EkMmVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0Zfdi8lJmZyYW1lR0Zfdi8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRjcvJS1lcXVhbGNvbHVtbnNHRjcvJS1kaXNwbGF5c3R5bGVHRjcvJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dRJjAuOGVtRidGXnBGYXBGLw== 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; 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Denne gang skal alle parametrene v\303\246re konkrete! 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