| Type: | Package |
| Title: | Estimate and Test Exponential vs. Pareto Distributions |
| Version: | 0.1.1 |
| Maintainer: | Jiqiang Wu <charles.wu@utah.edu> |
| Description: | The programs were developed for estimation of parameters and testing exponential versus Pareto distribution during our work on hydrologic extremes. See Kozubowski, T.J., A.K. Panorska, F. Qeadan, and A. Gershunov (2007) <doi:10.1080/03610910802439121>, and Panorska, A.K., A. Gershunov, and T.J. Kozubowski (2007) <doi:10.1007/978-0-387-34918-3_26>. |
| BugReports: | https://github.com/jiqiaingwu/LREP/issues |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| Depends: | R (≥ 4.0.0) |
| RoxygenNote: | 7.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2021-08-17 03:36:22 UTC; Charles |
| Author: | Fares Qeadan [aut], Jiqiang Wu [aut, cre], Tomasz Kozubowski [aut], Anna Panorska [aut] |
| Repository: | CRAN |
| Date/Publication: | 2021-08-17 05:30:08 UTC |
LREP: Estimate and Test Exponential vs. Pareto Distributions
Description
The programs were developed for estimation of parameters and testing exponential versus Pareto distribution during our work on hydrologic extremes. See Kozubowski, T.J., A.K. Panorska, F. Qeadan, and A. Gershunov (2007) <doi:10.1080/03610910802439121>, and Panorska, A.K., A. Gershunov, and T.J. Kozubowski (2007) <doi:10.1007/978-0-387-34918-3_26>.
Details
We consider the problem of maximum likelihood estimation of the parameters of the Pareto Type II (Lomax) distribution. We show that in certain parametrization and after modification of the parameter space to include exponential distribution as a special case, the MLEs of parameters always exist. Moreover, the MLEs have a non standard asymptotic distribution in the exponential case due to the lack of regularity. Further, we develop a likelihood ratio test for exponentiality versus Pareto II distribution.
Author(s)
Maintainer: Jiqiang Wu charles.wu@utah.edu
Authors:
Fares Qeadan fares.qeadan@utah.edu
Tomasz Kozubowski tkozubow@unr.edu
Anna Panorska ania@unr.edu
References
Kozubowski, T.J., A.K. Panorska, F. Qeadan, and A. Gershunov (2007). Testing exponentiality versus Pareto distribution via likelihood ratio, preprint in review.
Panorska, A.K., A. Gershunov, and T.J. Kozubowski (2007). From diversity to volatility: Probability of daily precipitation and extremes. Nonlinear Dynamics in Geosciences (A. Tsonis and J. Elsner, Eds.), Springer, New York, pp 465-484.
See Also
Useful links:
Report bugs at https://github.com/jiqiaingwu/LREP/issues
This program takes your data and the significance level as input and returns the critical number for the test, the value of the -2L (deviance) statistic and the decision (Pareto or exponential) as output.
Description
This program takes your data and the significance level as input and returns the critical number for the test, the value of the -2L (deviance) statistic and the decision (Pareto or exponential) as output.
Usage
expparetotest(x, alpha)
Arguments
x |
Import Raw data |
alpha |
Significance level. Note: this program works only for the following significance levels: 0.10, 0.075, 0.05, 0.025, 0.01 and 0.005. |
Value
Output the critical number for the test, the value of the -2L (deviance) statistic and the decision (Pareto or exponential).
Fields
criticalCritical value
statisticDeviance statistic
infoInterpret the data is coming from an exponential distribution or Pareto distribution.
Examples
x<-rexp(1000,0.1)
print(expparetotest(x,0.05))
The program will take your data as input and return three numbers as output: estimate of s, estimate of alpha, and value of the statistic L.
Description
The program will take your data as input and return three numbers as output: estimate of s, estimate of alpha, and value of the statistic L.
Usage
sigmaalphaLREP(x, tolerance)
Arguments
x |
Import Raw data |
tolerance |
Tolerance quantity |
Value
Output three estimates by using maximum likelihood method
Fields
s.hatOutput estimate of s
a.hatestimate of alpha
log.like.ratiovalue of the statistic L
Examples
x<-rexp(1000,0.1)
print(sigmaalphaLREP(x,10^-12))