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Math 141 - Quantile-Quantile Plots

math 141 Quantile-Quantile PlotsAlbyn Jones11 Library jones/courses/141 Albyn JonesMath 141 Outline: Quantile-Quantile PlotsQuantiles and Order StatisticsQuantile- quantile PlotsNormal quantile PlotsAlbyn JonesMath 141 Quantiles 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 141 Order 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 92 102 105 106 109 110 Albyn JonesMath 141 Order 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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