zipfpssFit {zipfextR} | R Documentation |
Zipf-PSS parameters estimation.
Description
For a given sample of strictly positive integer numbers, usually of the type of ranking data or frequencies of frequencies data, estimates the parameters of the Zipf-PSS distribution by means of the maximum likelihood method. The input data should be provided as a frequency matrix.
Usage
zipfpssFit(data, init_alpha = NULL, init_lambda = NULL, level = 0.95,
isTruncated = FALSE, ...)
## S3 method for class 'zipfpssR'
residuals(object, isTruncated = FALSE, ...)
## S3 method for class 'zipfpssR'
fitted(object, isTruncated = FALSE, ...)
## S3 method for class 'zipfpssR'
coef(object, ...)
## S3 method for class 'zipfpssR'
plot(x, isTruncated = FALSE, ...)
## S3 method for class 'zipfpssR'
print(x, ...)
## S3 method for class 'zipfpssR'
summary(object, isTruncated = FALSE, ...)
## S3 method for class 'zipfpssR'
logLik(object, ...)
## S3 method for class 'zipfpssR'
AIC(object, ...)
## S3 method for class 'zipfpssR'
BIC(object, ...)
Arguments
data |
Matrix of count data in form of table of frequencies. |
init_alpha |
Initial value of |
init_lambda |
Initial value of |
level |
Confidence level used to calculate the confidence intervals (default 0.95). |
isTruncated |
Logical; if TRUE, the truncated version of the distribution is returned.(default = FALSE) |
... |
Further arguments to the generic functions. The extra arguments are passing to the optim function. |
object |
An object from class "zpssR" (output of zipfpssFit function). |
x |
An object from class "zpssR" (output of zipfpssFit function). |
Details
The argument data
is a two column matrix with the first column containing the observations and
the second column containing their frequencies.
The log-likelihood function is equal to:
where is the number of different values in the sample, being
is the absolute
frequency of
.The probabilities are calculated applying the Panjer recursion.
By default the initial values of the parameters are computed using the function
getInitialValues
.
The function optim is used to estimate the parameters.
Value
Returns a zpssR object composed by the maximum likelihood parameter estimations jointly with their standard deviation and confidence intervals and the value of the log-likelihood at the maximum likelihood estimator.
References
Panjer, H. H. (1981). Recursive evaluation of a family of compound distributions. ASTIN Bulletin: The Journal of the IAA, 12(1), 22-26.
Sundt, B., & Jewell, W. S. (1981). Further results on recursive evaluation of compound distributions. ASTIN Bulletin: The Journal of the IAA, 12(1), 27-39.
See Also
Examples
data <- rzipfpss(100, 2.5, 1.3)
data <- as.data.frame(table(data))
data[,1] <- as.numeric(as.character(data[,1]))
data[,2] <- as.numeric(as.character(data[,2]))
initValues <- getInitialValues(data, model='zipfpss')
obj <- zipfpssFit(data, init_alpha = initValues$init_alpha, init_lambda = initValues$init_lambda)