Beta Distribution

library(ggplot2)
library(reshape2)
x <- seq(0,1,length=21)
beta_dist <- data.frame(cbind(x, dbeta(x,1,4), dbeta(x,2,8),dbeta(x,20,80)))

The probability density for Beta Distribution with different parameters are as follows:

colnames(beta_dist) <- c("x","a=1 b=4","a=2 b=8","a=20 b=80")
beta_dist

##       x a=1 b=4   a=2 b=8 a=20 b=80
## 1  0.00  4.0000 0.000e+00 0.000e+00
## 2  0.05  3.4295 2.514e+00 2.844e-05
## 3  0.10  2.9160 3.444e+00 2.082e-01
## 4  0.15  2.4565 3.462e+00 5.048e+00
## 5  0.20  2.0480 3.020e+00 9.930e+00
## 6  0.25  1.6875 2.403e+00 4.207e+00
## 7  0.30  1.3720 1.779e+00 5.772e-01
## 8  0.35  1.0985 1.235e+00 3.095e-02
## 9  0.40  0.8640 8.062e-01 7.020e-04
## 10 0.45  0.6655 4.933e-01 6.807e-06
## 11 0.50  0.5000 2.813e-01 2.706e-08
## 12 0.55  0.3645 1.480e-01 4.017e-11
## 13 0.60  0.2560 7.078e-02 1.909e-14
## 14 0.65  0.1715 3.011e-02 2.291e-18
## 15 0.70  0.1080 1.102e-02 4.816e-23
## 16 0.75  0.0625 3.296e-03 9.924e-29
## 17 0.80  0.0320 7.373e-04 7.471e-36
## 18 0.85  0.0135 1.046e-04 3.187e-45
## 19 0.90  0.0040 6.480e-06 1.158e-58
## 20 0.95  0.0005 5.344e-08 5.354e-82
## 21 1.00  0.0000 0.000e+00 0.000e+00

beta_dist <- melt(beta_dist,x)
g <- ggplot(beta_dist, aes(x,value, color=variable))
g+geom_line() + labs(title="Beta Distribution") + labs(x="Probability", y="Probability for Probability")