How to calculate the inverse cumulative beta distribution function in java

Question

I am looking for a java library / implementation which supports the calculation of the inverse cumulative distribution function for the beta distribution (aka estimation of quantiles) with reasonable precision.

Of course I have tried apache commons math, but in version 3 there still seem to be some issues with the precision. Below the problem which lead to this question is described extensively.

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Suppose I want to calculate the credible interval of a beta distribution with a lot of trials. In apache commons math ...

final int trials = 161750;
final int successes = 10007;
final double alpha = 0.05d;

// the supplied precision is the default precision according to the source code
BetaDistribution betaDist = new BetaDistribution(successes + 1, trials - successes + 1, 1e-9);

System.out.println("2.5 percentile :" + betaDist.inverseCumulativeProbability(alpha / 2d));
System.out.println("mean: " + betaDist.getNumericalMean());
System.out.println("median: " + betaDist.inverseCumulativeProbability(0.5));
System.out.println("97.5 percentile :" + betaDist.inverseCumulativeProbability(1 - alpha / 2d));

which delivers

2.5 percentile :0.062030402074808505
mean: 0.06187249616697166
median: 0.062030258659508855
97.5 percentile :0.06305170793994147

The issues is that the 2.5 percentile and median are the same meanwhile both greater than the mean.

In comparison, the R-package binom delivers

binom.confint(10007+1,161750+2,methods=c("agresti-coull","exact","wilson"))
         method     x      n      mean      lower      upper
1 agresti-coull 10008 161752 0.0618725 0.06070873 0.06305707
2         exact 10008 161752 0.0618725 0.06070317 0.06305756
3        wilson 10008 161752 0.0618725 0.06070877 0.06305703

and the R-package stats

qbeta(c(0.025,0.975),10007+1,161750-10007+1)
[1] 0.06070355 0.06305171

To second the results from R, here is what Wolfram Alpha told me

• InverseBetaRegularized[0.025,10007+1,161750-10007+1] => 0.06070354631...
• InverseBetaRegularized[0.975,10007+1,161750-10007+1] => 0.06305170794...

Final note on the requirements:

• I need to run a lot of these calculations. Hence any solution should not take longer than 1s (which is still a lot compared to the 41ms of (albeit wrong) apache commons math).
• I am aware that one can use R within java. For reasons I won't elaborate here, this is the last option if anything else (pure java) fails.

Update 21.08.12

It seems that the issue has been fixed or at least improved in 3.1-SNAPSHOT of apache-commons-math. For the usecase above

2.5 percentile :0.06070354581340706
mean: 0.06187249616697166
median: 0.06187069085946604
97.5 percentile :0.06305170793994147

Update 23.02.13

While at first glance this question and it's responses may be too localized, I think that it very well illustrates that some numerical problems cannot be solved (efficiently) with a what-first-comes-to-mind-hacker-approach. So I hope it remains open.

Answer 1

The issue has been fixed in apache commons math 3.1.1

The testcase above delivered

2.5 percentile :0.06070354581334864
mean: 0.06187249616697166
median: 0.06187069085930821
97.5 percentile :0.0630517079399996

which matches the results from the r-package stats. Extensive application of 3.1-SNAPSHOT + x versions also did not cause any problems.