Re: test difference Kurtosis and skewness

In my last post there was a small mistiness, it should be:

Depending on the location I have between 300-1000 measurement pairs
(were pair revers to model/satellite meas. which are taken at the the
same time).

Klaus

Klaus wrote:
Ok, my problem is follwing:

I have to assimilate satellite derived soil moisture measurements into
a numerical weather prediction model. The problem is that the satellite
derived measurements can differ significantely from the model. For
example they can have a different absolute value or a different dynamic
range. So if I simply feed the satellite meas. without correction into
the model, they might mess up the whole model. A possible solution to
this problem is to match the CDF of the satellite meas. to the CDF of
the corresponding model parameter. So far the CDF matching was done by
a 3rd order polynomial which corrected the mean, variance skewness and
kurtosis. But I have (visually) observed that the skewness/kurtosis are
in most cases quite similiar anyway so I only would need to correct the
mean and variance. Of course it would be nice to underpin this
observation with some statistical evidence, espacially considering that
I have to run this CDF matching for thousands of points.

By the way both CDFs are from samples. Depending on the location I have
between 300-1000 measurements (taken at the same time). The mean and
the variance of the two CDFs can be quite different, the difference in
Kurtosis and Skewness are small.

Klaus



David Jones wrote:
Klaus wrote:
Yes I can calculate them. My actual problem is that I have to match
the CDF of one distribution to the other. Before I do this cdf
matching I want to know which moments I have to match, i.e. which
moments are significantly different.

Klaus


Eric B wrote:
If I have two distributions, how can I test if their kurtosis and
skewness are different?

Why do you need to test ? Can't you just calculate them and compare
?

Eric B.

You need to be more specific. From what you have said there are 3
possibilities for your distributions:

(i) both are theoretical (population) distributions;
(ii) one relates to a sample you have from an unknown distribution and
the other is a theoretical (population) distribution;
(iii) both relate to a samples you have from two (possibly different)
unknown distributions.

Indications of sample size and context (ie. why?) are also likely to
be useful. Have you tried a graphical approach?

David Jones

.

Relevant Pages

  • Re: test difference Kurtosis and skewness
    ... I have to assimilate satellite derived soil moisture measurements into ... this problem is to match the CDF of the satellite meas. ... the CDF of one distribution to the other. ...
    (sci.stat.math)
  • Re: test difference Kurtosis and skewness
    ... I have to assimilate satellite derived soil moisture measurements ... to the CDF of the corresponding model ... corrected the mean, variance skewness and kurtosis. ...
    (sci.stat.math)
  • Re: estimate the cdf 95% with a confidence interval of a 95%
    ... What BinomF, 0.95 MN) represents is the probability that of your ... distribution function for a binomial distribution, ... samples have a delay below x, so this would be the probability that X=x ... compute an estimate of the 95% cdf of such the delay, ...
    (sci.math)
  • Re: Demonstration that least squares give maximum likelihood
    ... Call the measurements m, m, ..., m. ... mean m and standard deviation sigma. ... It is generally accepted in our field that you can usually assume normality, partly because the errors have multiple causes. ... Another responder alluded to concerns that - outliers apart - there are suspicions that the tips of the tails of real analytical data distributions are bigger and longer than the tails of the normal distribution. ...
    (sci.stat.edu)
  • Re: estimate the cdf 95% with a confidence interval of a 95%
    ... samples have a delay below x, so this would be the probability that X=x ... the distribution from your data and then compute the percentile from the ... What I do is that every station writes in a file the delay that it took ... compute an estimate of the 95% cdf of such the delay, ...
    (sci.math)