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https://issues.apache.org/jira/browse/MATH-1373?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15338359#comment-15338359
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Brent Worden edited comment on MATH-1373 at 6/19/16 4:22 AM:
-------------------------------------------------------------
I am not completely convinced this change is correct.
Referencing on of the citations,
http://mathworld.wolfram.com/LogNormalDistribution.html, the density function
is parameterized the same way LogNormalDistribution is parameterized with
* MathWorld's M being equivalent to Commons Math's scale
* MathWorld's S being equivalent to Commons Math's shape
The distribution mean according to MathWorld is Exp(M + S^2 / 2) which
corresponds to Exp(scale + shape^2 / 2) and is how it is coded in
LogNormalDistribution.
Likewise, MathWorld states the distribution variance Exp(S^2 + 2 M) * (Exp(S^2
- 1) which is Exp(shape^2 + 2 scale) * (Exp(shape^2 - 1). Again, this matches
the implementation.
Furthermore, generating a large sample from the distribution results in sample
means and variances that are pretty close to the population values returned
from the getNumericalMean and getNumericalVariance methods. Here is the code I
am using to make that claim:
{code}
@Test
public void testMeanAndVariance() {
LogNormalDistribution dist = new LogNormalDistribution(5.375, 1.125);
double[] x = new double[100000];
for (int i = 0; i < x.length; ++i) {
x[i] = dist.inverseCumulativeProbability(Math.random());
}
double actualMean = new Mean().evaluate(x);
double actualVariance = new Variance().evaluate(x);
double expectedMean = dist.getNumericalMean();
double expectedVariance = dist.getNumericalVariance();
System.out.println(String.format("Mean: %f vs %f (actual vs expected)",
actualMean, expectedMean));
System.out.println(String.format("Variance: %f vs %f (actual vs
expected)", actualVariance, expectedVariance));
}
{code}
was (Author: brentworden):
I am not completely convinced this change is correct.
Referencing on of the citations,
http://mathworld.wolfram.com/LogNormalDistribution.html, the density function
is parameterized the same way LogNormalDistribution is parameterized with
* MathWorld's M being equivalent to Commons Math's scale
* MathWorld's S being equivalent to Commons Math's shape
The distribution mean according to MathWorld is Exp(M + S^2 / 2) which
corresponds to Exp(scale + shape^2 / 2) and is how it is coded in
LogNormalDistribution.
Likewise, MathWorld states the distribution variance Exp(S^2 + 2 M) * (Exp(S^2
- 1) which is Exp(shape^2 + 2 scale) * (Exp(shape^2 - 1). Again, this matches
the implementation.
Furthermore, generating a large sample from the distribution results in sample
means and variances that are pretty close to the expected values returned from
the getNumericalMean and getNumericalVariance methods. Here is the code I am
using to make that claim:
{code}
@Test
public void testMeanAndVariance() {
LogNormalDistribution dist = new LogNormalDistribution(5.375, 1.125);
double[] x = new double[100000];
for (int i = 0; i < x.length; ++i) {
x[i] = dist.inverseCumulativeProbability(Math.random());
}
double actualMean = new Mean().evaluate(x);
double actualVariance = new Variance().evaluate(x);
double expectedMean = dist.getNumericalMean();
double expectedVariance = dist.getNumericalVariance();
System.out.println(String.format("Mean: %f vs %f (actual vs expected)",
actualMean, expectedMean));
System.out.println(String.format("Variance: %f vs %f (actual vs
expected)", actualVariance, expectedVariance));
}
{code}
> In LogNormalDistribution.java, it appears shape & scale are
> reversed/mis-labelled.
> ----------------------------------------------------------------------------------
>
> Key: MATH-1373
> URL: https://issues.apache.org/jira/browse/MATH-1373
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.6.1
> Reporter: Karl D. Gierach
> Priority: Minor
> Attachments: MATH-1373.patch
>
> Original Estimate: 1h
> Remaining Estimate: 1h
>
> When I compute the logshape and log scale based on the formulas on
> wikipedia's lognormal distribution page that use empirical mean and variance,
> I found that the getNumericalMean() method was not returning the empirical
> mean.
> However, upon just trying to reverse the shape and scale parameters in the
> constructor proved to fix the problem, and the object then returns the
> correct empirical mean.
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