Unit Half Logistic-Geometry distribution

The Unit Half Logistic-Geometry family

UHLG(mu.link = "log")

Arguments

mu.link: defines the mu.link, with "log" link as the default for the mu parameter.

Value

Returns a gamlss.family object which can be used to fit a UHLG distribution in the gamlss() function.

Details

The Unit Half Logistic-Geometry distribution with parameter mu, has density given by

\(f(x| \mu) = \frac{2 \mu}{(\mu+(2-\mu)x)^2} \)

for \(0 < x < 1\) and \(\mu > 0\).

References

Ramadan, A. T., Tolba, A. H., & El-Desouky, B. S. (2022). A unit half-logistic geometric distribution and its application in insurance. Axioms, 11(12), 676.

Author

Juan Diego Suarez Hernandez, jsuarezhe@unal.edu.co

Examples

# Example 1
# Generating some random values with
# known mu
y <- rUHLG(n=500, mu=7)

# Fitting the model
library(gamlss)
mod1 <- gamlss(y~1, family=UHLG,
               control=gamlss.control(n.cyc=500, trace=FALSE))

# Extracting the fitted values for mu, sigma and nu
# using the inverse link function
exp(coef(mod1, what="mu"))
#> (Intercept) 
#>    7.453204 

# Example 2
# Generating random values under some model

# A function to simulate a data set with Y ~ UHLG
gendat <- function(n) {
  x1 <- runif(n, min=0.4, max=0.6)
  x2 <- runif(n, min=0.4, max=0.6)
  mu    <- exp(-0.5 + 3*x1 - 2.5*x2)
  y <- rUHLG(n=n, mu=mu)
  data.frame(y=y, x1=x1, x2=x2)
}

datos <- gendat(n=5000)

mod2 <- gamlss(y~x1+x2,
               family=UHLG, data=datos,
               control=gamlss.control(n.cyc=500, trace=TRUE))
#> GAMLSS-RS iteration 1: Global Deviance = -1433.922 
#> GAMLSS-RS iteration 2: Global Deviance = -1433.922 
summary(mod2)
#> Warning: summary: vcov has failed, option qr is used instead
#> ******************************************************************
#> Family:  c("UHLG", "Unit Half Logistic-Geometry") 
#> 
#> Call:  
#> gamlss(formula = y ~ x1 + x2, family = UHLG, data = datos, control = gamlss.control(n.cyc = 500,  
#>     trace = TRUE)) 
#> 
#> Fitting method: RS() 
#> 
#> ------------------------------------------------------------------
#> Mu link function:  log
#> Mu Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  -0.5902     0.3047  -1.937   0.0528 .  
#> x1            3.2639     0.4331   7.536 5.74e-14 ***
#> x2           -2.4966     0.4301  -5.805 6.83e-09 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> ------------------------------------------------------------------
#> No. of observations in the fit:  5000 
#> Degrees of Freedom for the fit:  3
#>       Residual Deg. of Freedom:  4997 
#>                       at cycle:  2 
#>  
#> Global Deviance:     -1433.922 
#>             AIC:     -1427.922 
#>             SBC:     -1408.371 
#> ******************************************************************