EfficientClosedGPD

The R package EfficientClosedGPD provides some efficient closed form estimators of the parameters of the Generalized Pareto Distribution proposed in From and Ratnasingam (2022). Please see the examples below.

rm(list = ls())
library(devtools) # Make sure that the devtools library is loaded
install_github("suthakaranr/EfficientClosedGPD")
library(EfficientClosedGPD)  # Load the package 
set.seed(650) 
x = rgpd2(40, 2, 2) # Generate sample
Method1(x) # Method M1
Method2(x) # Method M2
Method3(x) # Method M3
MethodQM(x) # Method QM
MethodPOS(x) # Method POS
MethodLCVM(x) # Method LCVM

IneqBetaFun

The R package IneqBetaFun provides several new upper and lower bounds for the Beta function and the quotient of Beta functions proposed in From and Ratnasingam (2022). Please see the examples below.

rm(list = ls())
library(devtools) # Make sure that the devtools library is loaded
install_github("suthakaranr/IneqBetaFun")
library(IneqBetaFun)

them_3_1(1/2, 1/2) # Theorem 3.1
them_3_2(1/2,1/2) # Theorem 3.2
them_3_3(1/2,1/2) # Theorem 3.3
them_3_4(1/2,1/2) # Theorem 3.4
them_3_5(2,2) # Theorem 3.5
them_3_6(2,2) # Theorem 3.6
them_3_7(0.25,0.5) # Theorem 3.7: Case 1
them_3_7(0.5,1) # Theorem 3.7: Case 2
them_3_8(2,2) # Theorem 3.8
them_3_10(4,2) # Theorem 3.10: Case 1
them_3_10(4,3.5) # Theorem 3.10: Case 2
them_3_11a(4,2) # Theorem 3.11: Case 1
them_3_11b(5,5) # Theorem 3.11: Case 2
corollary_2(1, 1.5) # Corollary 2
them_3_14(1,2) # Theorem 3.14
them_3_15(1,2) # Theorem 3.15

# Ratios of Beta Functions

them_3_9(0.5,0.75) # Theorem 3.9: Case 1: x1 <= x2
them_3_9(1.5,1) # Theorem 3.9: Case 2: x1 > x2
them_3_17(1, 1.5, 2) # Theorem 3.17
corollary_ratio_1(1, 1.5,2, 3) # Corollary 1
them_3_13(1, 1.5,2) # Theorem 3.13
them_3_16(1, 1.5,2) # Theorem 3.16
them_3_17(1, 1.5,2) # Theorem 3.17