Math 141 - Quantile-Quantile Plots

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math 141Quantile- quantile PlotsAlbyn Jones11Library jones/courses/141Albyn JonesMath 141Outline: Quantile-Quantile PlotsQuantiles and Order StatisticsQuantile- quantile PlotsNormal quantile PlotsAlbyn JonesMath 141Quantiles and Order StatisticsDefinition: p-th quantileqpEarlier we defined the p-th quantile of the distribution of a RVXas any numberqpsatisfyingP(X qp) pandP(X qp) (1 p).Albyn JonesMath 141Order StatisticsSample quantiles are based onOrder Statistics:LetX1,X2,...,Xnbe a sample of sizen. Theorder statisticsX(1),X(2),...,X(n)are just the observations sorted intoascending order.# The data> x[1] 76 92 83 105 102 109 106 91 110 89# The order statistics> sort(x)[1] 76 83 89 91 92 102 105 106 109 110Albyn JonesMath 141Order Statistics and Sample QuantilesThere are numerous definitions of sample quantiles chosen toperform well under various conditions.

The QQ plot The quantile–quantile plot, or QQplot, is a simple graphical method for comparing two sets of sample quantiles. Plot the pairs of order statistics (X (k);Y (k)): If the two datasets come from the same distribution, the points ... Math 141 - Quantile-Quantile Plots ...

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