Bivariate Beta distribution
I am analyzing two dimensional data. After analyzing each dimension with the help of the fitdistrplus and logspline packages, they both fit the Beta distribution. Is it possible to analyze the two dimensional data like a bivariate Beta distribution? (Note: I am using R.)
Sample of data set:
The data points are outputs from 2 different chemical reaction test conducted over time on a particular product. So at time 1 PB=2.394 and DBA=134.417, at time 2 PB=2.594 and DBA=111.382 and so on.
structure(list(PB = c(2.394, 2.594, 2.78, 2.499, 2.478, 2.744,
2.563, 2.553, 2.631, 2.434, 2.604, 2.685, 2.439, 2.548, 2.778,
2.604, 2.638, 2.585, 2.808, 2.784, 2.489, 2.797, 2.619, 2.687,
2.624, 2.341, 2.712, 2.493, 2.616, 2.562), DBA = c(134.417, 111.382,
125.303, 163.445, 89.428, 141.881, 140.559, 141.408, 122.498,
128.099, 115.88, 111.83, 170.685, 89.956, 128.948, 131.064, 170.114,
101.843, 132.092, 173.86, 91.976, 130.882, 132.016, 157.143,
122.052, 100.08, 140.079, 144.167, 141.072, 143.787)), .Names = c("PB",
"DBA"), row.names = c(NA, 30L), class = "data.frame")
Scaled sample data set for Beta distribution:
structure(list(PB = c(0.589027911453321, 0.781520692974013, 0.960538979788258,
0.690086621751685, 0.669874879692012, 0.925890279114534, 0.751684311838306,
0.742059672762271, 0.817131857555342, 0.627526467757459, 0.791145332050048,
0.869104908565929, 0.632338787295477, 0.737247353224254, 0.958614051973051,
0.791145332050048, 0.823869104908566, 0.772858517805582, 0.987487969201155,
0.964388835418672, 0.68046198267565, 0.976900866217517, 0.8055822906641,
0.871029836381136, 0.810394610202118, 0.538017324350337, 0.895091434071223,
0.684311838306064, 0.80269489894129, 0.750721847930703), NOH = c(0.371624288211084,
0.241754524440435, 0.320240175903479, 0.535282178496927, 0.117979365168856,
0.413705812707899, 0.406252466595253, 0.411039070868805, 0.304425776625134,
0.336003833793764, 0.267113942605852, 0.244280317979365, 0.576100806224277,
0.120956193268309, 0.340790438067317, 0.352720302193156, 0.572881547048543,
0.18797429103005, 0.358516096295879, 0.594001240345042, 0.13234481592152,
0.351694198567965, 0.358087613463382, 0.499751930991712, 0.301911258950217,
0.17803461690252, 0.403546259232114, 0.426594125274849, 0.409144725714608,
0.424451711112364)), .Names = c("PB", "NOH"), row.names = c(NA,
30L), class = "data.frame")
Sample of data set:
The data points are outputs from 2 different chemical reaction test conducted over time on a particular product. So at time 1 PB=2.394 and DBA=134.417, at time 2 PB=2.594 and DBA=111.382 and so on.
structure(list(PB = c(2.394, 2.594, 2.78, 2.499, 2.478, 2.744,
2.563, 2.553, 2.631, 2.434, 2.604, 2.685, 2.439, 2.548, 2.778,
2.604, 2.638, 2.585, 2.808, 2.784, 2.489, 2.797, 2.619, 2.687,
2.624, 2.341, 2.712, 2.493, 2.616, 2.562), DBA = c(134.417, 111.382,
125.303, 163.445, 89.428, 141.881, 140.559, 141.408, 122.498,
128.099, 115.88, 111.83, 170.685, 89.956, 128.948, 131.064, 170.114,
101.843, 132.092, 173.86, 91.976, 130.882, 132.016, 157.143,
122.052, 100.08, 140.079, 144.167, 141.072, 143.787)), .Names = c("PB",
"DBA"), row.names = c(NA, 30L), class = "data.frame")
Scaled sample data set for Beta distribution:
structure(list(PB = c(0.589027911453321, 0.781520692974013, 0.960538979788258,
0.690086621751685, 0.669874879692012, 0.925890279114534, 0.751684311838306,
0.742059672762271, 0.817131857555342, 0.627526467757459, 0.791145332050048,
0.869104908565929, 0.632338787295477, 0.737247353224254, 0.958614051973051,
0.791145332050048, 0.823869104908566, 0.772858517805582, 0.987487969201155,
0.964388835418672, 0.68046198267565, 0.976900866217517, 0.8055822906641,
0.871029836381136, 0.810394610202118, 0.538017324350337, 0.895091434071223,
0.684311838306064, 0.80269489894129, 0.750721847930703), NOH = c(0.371624288211084,
0.241754524440435, 0.320240175903479, 0.535282178496927, 0.117979365168856,
0.413705812707899, 0.406252466595253, 0.411039070868805, 0.304425776625134,
0.336003833793764, 0.267113942605852, 0.244280317979365, 0.576100806224277,
0.120956193268309, 0.340790438067317, 0.352720302193156, 0.572881547048543,
0.18797429103005, 0.358516096295879, 0.594001240345042, 0.13234481592152,
0.351694198567965, 0.358087613463382, 0.499751930991712, 0.301911258950217,
0.17803461690252, 0.403546259232114, 0.426594125274849, 0.409144725714608,
0.424451711112364)), .Names = c("PB", "NOH"), row.names = c(NA,
30L), class = "data.frame")
Комментарии
Отправить комментарий