On generalized log-Moyal distribution: A new heavy tailed size distribution

New methods to define heavy-tailed distributions with applications to insurance data

“…library(AdequacyModel) data<-read.csv(file.choose(), header=TRUE) data=data[,1] data=data[!is.na(data)] data=data/1000 data pdf_pm <-function(par,x) { a= par [1] t= par [2] g= par [3] a * t * g * (x^(a-1)) * exp((g * x^a)/(t+g * x^a)) * (1/(t+g * x^a)^2) * (1/(exp(1)-1)) } cdf_pm <-function(par,x) { a= par [1] t= par [2] g= par [3] (exp((g * x^a)/(t+g * x^a))-1)/(exp(1)-1) } set.seed(0) goodness.fit(pdf=pdf_pm,cdf=cdf_pm, starts = c(0.1,0.1,0.1), data = data, method="B", domain=c(0,Inf),mle=NULL) ############################################################### R Code for Simulation ############################################################### ############################################################### ########## Generating a Random Sample of Size n from the EP-Weibull ############################################################### rEP_Weibull=function(par,n) { a=par [1]; t=par [2];g=par [3] u=runif(n) x=c() for (i in 1:n) { x[i]=((g/t) * (((log(u[i] * (exp(1)-1)+1))^(-1)-1)))^(-1/a) } return(x) } ############################################################### ##########…”

“…The pdf of the EP-Weibull ############################################################### dEP_Weibull <-function(par,x) { a= par [1] t= par [2] g= par [3] a * t * g * (x^(a-1)) * exp((g * x^a)/(t+g * x^a)) * (1/(t+g * x^a)^2) * (1/(exp(1)-1)) } ############################################################### ##########…”

“…The cdf of the EP-Weibull ############################################################### pEP_Weibull<-function(par,x) { a= par [1] t= par [2] g= par [3] ( n=seq (25,750,25) ############################################################### ########## Plots of Parameters ###############################################################…”

“…The Lomax and Burr-XII (B-XII) distributions are prominent competitors for modelling large losses and offer a wide range of applications in financial sciences. The proposed EP-W model is also compared with the GLM distribution of Bhati and Ravi [1]. We also considered the fiveparameter non-nested GOBXIII-W distribution of Haq et al [31].…”

“…Classical distributions are not flexible enough to cater such heavy-tailed data sets. For example, (i) the Pareto distribution, which is widely used in modelling financial data sets, does not provide a reasonable fit for many applications and (ii) the Weibull model covers better the behaviour of small losses, but fails to cover the behaviour of large losses; see Bhati and Ravi [1]. In such situation, heavy-tailed distributions are reliable and accurate candidate models to employ.…”