The function CJ2() defines The two-parameter Chris-Jerry distribution,
a two parameter distribution, for a gamlss.family object to be used
in GAMLSS fitting using the function gamlss().
Value
Returns a gamlss.family object which can be used to fit a CJ2 distribution in the gamlss() function.
Details
The two-parameter Chris-Jerry distribution with parameters mu and sigma
has density given by
\( f(x; \sigma, \mu) = \frac{\mu^2}{\sigma \mu + 2} (\sigma + \mu x^2) e^{-\mu x}; \quad x > 0, \quad \mu > 0, \quad \sigma > 0 \)
Note: In this implementation we changed the original parameters \(\theta\) for \(\mu\) and \(\lambda\) for \(\sigma\) we did it to implement this distribution within gamlss framework.
References
Chinedu, Eberechukwu Q., et al. "New lifetime distribution with applications to single acceptance sampling plan and scenarios of increasing hazard rates" Symmetry 15.10 (2023): 188.
Author
Manuel Gutierrez Tangarife, mgutierrezta@unal.edu.co
Examples
# Example 1
# Generating some random values with
# known mu and sigma
y <- rCJ2(n=500, mu=1, sigma=1.5)
# Fitting the model
require(gamlss)
mod1 <- gamlss(y~1, sigma.fo=~1, family=CJ2,
control=gamlss.control(n.cyc=5000, trace=TRUE))
#> GAMLSS-RS iteration 1: Global Deviance = 1717.116
#> GAMLSS-RS iteration 2: Global Deviance = 1716.058
#> GAMLSS-RS iteration 3: Global Deviance = 1715.707
#> GAMLSS-RS iteration 4: Global Deviance = 1715.582
#> GAMLSS-RS iteration 5: Global Deviance = 1715.536
#> GAMLSS-RS iteration 6: Global Deviance = 1715.519
#> GAMLSS-RS iteration 7: Global Deviance = 1715.513
#> GAMLSS-RS iteration 8: Global Deviance = 1715.51
#> GAMLSS-RS iteration 9: Global Deviance = 1715.509
#> GAMLSS-RS iteration 10: Global Deviance = 1715.509
# Extracting the fitted values for mu, sigma, nu and tau
# using the inverse link function
exp(coef(mod1, what="mu"))
#> (Intercept)
#> 1.025991
exp(coef(mod1, what="sigma"))
#> (Intercept)
#> 1.441409
# Example 2
# Generating random values under some model
gendat <- function(n) {
x1 <- runif(n, min=0, max=5)
x2 <- runif(n, min=0, max=5)
mu <- exp(-0.2 + 1.5 * x1)
sigma <- exp(1 - 0.7 * x2)
y <- rCJ2(n=n, mu, sigma)
data.frame(y=y, x1=x1, x2=x2)
}
set.seed(123)
datos <- gendat(n=500)
mod2 <- gamlss(y~x1, sigma.fo=~x2, family=CJ2, data=datos,
control=gamlss.control(n.cyc=5000, trace=TRUE))
#> GAMLSS-RS iteration 1: Global Deviance = -2211.964
#> GAMLSS-RS iteration 2: Global Deviance = -2213.243
#> GAMLSS-RS iteration 3: Global Deviance = -2213.713
#> GAMLSS-RS iteration 4: Global Deviance = -2213.887
#> GAMLSS-RS iteration 5: Global Deviance = -2213.948
#> GAMLSS-RS iteration 6: Global Deviance = -2213.97
#> GAMLSS-RS iteration 7: Global Deviance = -2213.978
#> GAMLSS-RS iteration 8: Global Deviance = -2213.981
#> GAMLSS-RS iteration 9: Global Deviance = -2213.982
summary(mod2)
#> Warning: summary: vcov has failed, option qr is used instead
#> ******************************************************************
#> Family: c("CJ2", "a two-parameter\n Chris-Jerry distribution")
#>
#> Call:
#> gamlss(formula = y ~ x1, sigma.formula = ~x2, family = CJ2, data = datos,
#> control = gamlss.control(n.cyc = 5000, trace = TRUE))
#>
#> Fitting method: RS()
#>
#> ------------------------------------------------------------------
#> Mu link function: log
#> Mu Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.22632 0.05892 -3.841 0.000138 ***
#> x1 1.51252 0.02380 63.556 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> ------------------------------------------------------------------
#> Sigma link function: log
#> Sigma Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.0639 0.5649 1.883 0.060217 .
#> x2 -0.6515 0.1850 -3.521 0.000469 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> ------------------------------------------------------------------
#> No. of observations in the fit: 500
#> Degrees of Freedom for the fit: 4
#> Residual Deg. of Freedom: 496
#> at cycle: 9
#>
#> Global Deviance: -2213.982
#> AIC: -2205.982
#> SBC: -2189.123
#> ******************************************************************