pearsonMSC | R Documentation |
This function performs (as pearsonFitML
) an ML estimation
for all sub-classes of the Pearson distribution system via numerical
optimization (with nlminb
) for model selection purposes.
Apart from calculating the log-likelihood values as well as the values of
some common model selection criteria (pure ML, AIC, AICc, BIC, HQC) for the
different sub-classes, model selection is done for each of the criteria and
the parameter estimates for each distribution sub-class are returned.
pearsonMSC(x, ...)
x |
empirical data (numerical vector) for MLE. |
... |
parameters for |
For the ML estimation, see the details of pearsonFitML
.
The considered Model Selection Criteria (MSCs) are 'pure' Maximum Likelihood
(ML
), Akaike Information Criterion (AIC
), corrected AIC
(AICc
), Bayes Information Criterion (BIC
, also known as Schwarz
Criterion), and Hannan-Quinn-Criterion (HQC
). The definitions used
for the different MSCs are
for ML
: -2\cdot \ln L(\theta)
for AIC
: -2\cdot \ln L(\theta)+2\cdot k
for AICc
: -2\cdot \ln L(\theta)+2\cdot k\cdot\frac{n}{n-k-1}
for BIC
: -2\cdot \ln L(\theta)+ k\cdot \ln(n)
for HQC
: -2\cdot \ln L(\theta)+2\cdot k\cdot \ln(\ln(n))
where \ln L(\theta)
denotes the log-Likelihood,
n
denotes the number of observations (ie, the length of x
)
and k
denotes the number of parameters of the distribution
(sub-class).
The best model minimizes the corresponding MSC function values.
A list containing
MSCs |
a matrix with rows |
logLik |
a vector with the log-likelihood values for the different distribution types. |
FittedDistributions |
a list with vectors of the parameter estimates (preceeded by the distribution type number) for the 8 Pearson distribution sub-classes. |
Best |
a list with components |
The implementation is still preliminary (and slow). No analytical results are used, ie. no analytical solutions for ML estimators and no analytical gradients.
Martin Becker martin.becker@mx.uni-saarland.de
PearsonDS-package
,
Pearson
,
pearsonFitML
## Generate sample
DATA <- rpearson(500,moments=c(mean=1,variance=2,skewness=1,kurtosis=5))
## Call pearsonMSC for model selection
MSC <- pearsonMSC(DATA,control=list(iter.max=1e5,eval.max=1e5))
## log-Likelihood values for all distribution sub-classes
print(MSC$logLik)
## Values for all MSCs and distribution sub-classes
print(MSC$MSCs)
## Model selection for all MSCs
print(MSC$Best)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.