[R] lmom package - Resending the email

[peter dalgaard]

lmom is based on L-moments, which are different from ordinary moments, except for the 1st one. It would be truly miraculous if it gave the same result as the ordinary method of moments or maximum likelihood. 

Estimates of any distributional parameter requires that the model actually fits the data, and in your case a qqnorm(amounts) shows that they are certainly not normal. In such cases, the L-moment estimator of the std.dev. is not necessarily an estimate of the std.dev. of the actual distribution.

A lognormal distribution seems to fit the data better. However, the L-moments suggest a value for zeta (the lower bound) of 3226 which is well inside the range of the actual data. In fact there are 16 observations that are less than 3226. Maximum likelihood would never do that, but the same sort of effect is well-known for the ordinary method of moments.

In short, you need to study the theory before you appply its results.

- Peter D.


On 03 Dec 2014, at 10:57 , Simon Zehnder <szehnder at uni-bonn.de> wrote:

> Katherine,
> 
> for a deeper understanding of differing values it makes sense to provide the list at least with an online description of the corresponding functions used in Minitab and SPSS…
> 
> Best 
> Simon
> On 03 Dec 2014, at 10:45, Katherine Gobin via R-help <r-help at r-project.org> wrote:
> 
>> Dear R forum
>> I sincerely apologize as my earlier mail with the captioned subject, since all the values got mixed up and the email is not readable. I am trying to write it again. 
>> My problem is I have a set of data and I am trying to fit some distributions to it. As a part of this exercise, I need to find out the parameter values of various distributions e.g. Normal distribution, Log normal distribution etc. I am using lmom package to do the same, however the parameter values obtained using lmom pacakge differ to a large extent from the parameter values obtained using say MINITAB and SPSS as given below -
>> _____________________________________________
>> 
>> amounts =  c(38572.5599129508,11426.6705314315,21974.1571641187,118530.32782443,3735.43055996748,66309.5211176106,72039.2934132668,21934.8841708626,78564.9136114375,1703.65825161293,2116.89180930203,11003.495671332,19486.3296339113,1871.35861218795,6887.53851253407,148900.978055447,7078.56497101651,79348.1239806592,20157.6241066905,1259.99802108593,3934.45912233674,3297.69946631591,56221.1154121067,13322.0705174134,45110.2498756567,31910.3686613912,3196.71168501252,32843.0140437202,14615.1499458453,13013.9915051561,116104.176753387,7229.03056392023,9833.37962177814,2882.63239493673,165457.372543821,41114.066453219,47188.1677766245,25708.5883755617,82703.7378298092,8845.04197017415,844.28834047836,35410.8486123933,19446.3808445684,17662.2398792892,11882.8497070776,4277181.17817307,30239.0371267968,45165.7512343364,22102.8513746687,5988.69296597127,51345.0146170238,1275658.35495898,15260.4892854214,8861.76578480635,37647.1638704867,4979.53544046949,7012.48134772332,3385.20612391205,1911.03114395959,66886.5036605189,2223.47536156462,814.947809578378,234.028589468841,5397.4347625133,13346.3226579065,28809.3901352898,6387.69226236731,5639.42730553242,2011100.92675507,4150.63707173462,34098.7514446498,3437.10672573502,289710.315303182,8664.66947305203,13813.3867161134,208817.521491857,169317.624400274,9966.78447705792,37811.1721605562,2263.19211279927,80434.5581206454,19057.8093104899,24664.5067589624,25136.5042354789,3582.85741610706,6683.13898432794,65423.9991390846,134848.302304064,3018.55371579808,546249.641168158,172926.689143006,3074.15064180208,1521.70624812788,59012.4248281661,21226.928522236,17572.5682970983,226.646947337851,56232.2982652019,14641.0043361533,6997.94414914865)
>> 
>> library(lmom)
>> lmom  =  samlmu(amounts)
>> # __________________________________________________________________
>> # Normal Distribution parameters
>> parameters_of_NOR  <- pelnor(lmom); parameters_of_NOR
>> 
>>      mu          sigma 115148.4    175945.8
>>                      Location       Scale     Minitab         115148.4     485173SPSS           115148.4     485173
>> # __________________________________________________________________
>> # Log Normal (3 Parameter) Distribution parameters
>>       zeta                mu               sigma 3225.798890    9.114879      2.240841
>>                              Location            Scale           Shape
>> MINITAB               9.73361             1.76298      75.51864SPSS                    9.7336                1.763          75.519           # __________________________________________________________________
>> 
>> Besides Genaralized extreme Value distributions, all the other distributions e.g. Gamma, Exponential (2 parameter) distributions etc give different results than MINITAB and SPSS.
>> Can some one guide me?
>> 
>> Regards
>> Katherine
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>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com