NEE: New Exponentiated Exponential family

In ousuga/RelDists: Estimation for some Reliability Distributions

New Exponentiated Exponential family

Description

The function NEE() defines the New Exponentiated Exponential distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

NEE(mu.link = "log", sigma.link = "log")

Arguments

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

Details

The New Exponentiated Exponential distribution with parameters mu and sigma has density given by

f(x | \mu, \sigma) = \log(2^\sigma) \mu \exp(-\mu x) (1-\exp(-\mu x))^{\sigma-1} 2^{(1-\exp(-\mu x))^\sigma},

for x>0, \mu>0 and \sigma>0.

Note: In this implementation we changed the original parameters \theta for \mu and \alpha for \sigma, we did it to implement this distribution within gamlss framework.

Value

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

References

Hassan, Anwar, I. H. Dar, and M. A. Lone. "A New Class of Probability Distributions With An Application to Engineering Data." Pakistan Journal of Statistics and Operation Research 20.2 (2024): 217-231.

See Also

dNEE

Examples

# Example 1
# Generating some random values with
# known mu and sigma
y <- rNEE(n=500, mu=2.5, sigma=3.5)

# Fitting the model
require(gamlss)

mod1 <- gamlss(y~1, sigma.fo=~1, family=NEE,
               control=gamlss.control(n.cyc=5000, trace=TRUE))

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

# Example 2
# Generating random values under some model
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu <- exp(-0.2 + 1.5 * x1)
  sigma <- exp(1 - 0.7 * x2)
  y <- rNEE(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=NEE, data=datos,
               control=gamlss.control(n.cyc=5000, trace=TRUE))

summary(mod2)

# Example 3  --------------------------------------------------
# Obtained from Hassan (2024) page 226
# The data set consists of 63 observations of the gauge lengths of 10mm. 

y <- c(1.901, 2.132, 2.203, 2.228, 2.257, 2.350, 2.361, 2.396, 2.397, 
       2.445, 2.454, 2.474, 2.518, 2.522, 2.525, 2.532,  2.575, 2.614, 
       2.616, 2.618, 2.624, 2.659, 2.675, 2.738, 2.740, 2.856, 2.917, 
       2.928, 2.937, 2.937, 2.977, 2.996,  3.030, 3.125, 3.139, 3.145, 
       3.220, 3.223, 3.235, 3.243, 3.264, 3.272, 3.294, 3.332, 3.346, 
       3.377, 3.408, 3.435,  3.493, 3.501, 3.537, 3.554, 3.562, 3.628, 
       3.852, 3.871, 3.886, 3.971, 4.024, 4.027, 4.225, 4.395, 5.020)

mod3 <- gamlss(y~1, family=NEE)

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod3, what="mu"))
exp(coef(mod3, what="sigma"))

# Hist and estimated pdf
hist(y, freq=FALSE, ylim=c(0, 0.7))
curve(dNEE(x, mu=2.076862, sigma=255.2289), 
      add=TRUE, col="tomato", lwd=2)

# Empirical cdf and estimated ecdf
plot(ecdf(y))
curve(pNEE(x, mu=2.076862, sigma=255.2289), 
      add=TRUE, col="tomato", lwd=2)
# QQplot
qqplot(y, rNEE(n=length(y), mu=2.076862, sigma=255.2289), col="tomato")
qqline(y, distribution=function(p) qNEE(p, mu=2.076862, sigma=255.2289))

# Example 4  --------------------------------------------------
# Obtained from Hassan (2024) page 226
# The dataset was reported by Bader and Priest (1982) on failure 
# stresses (in GPa) of 65 single carbon fibers of lengths 50 mm

y <- c(0.564, 0.729, 0.802, 0.95, 1.053, 1.111, 1.115, 1.194, 1.208,
       1.216, 1.247, 1.256, 1.271, 1.277, 1.305, 1.313, 1.348, 
       1.39, 1.429, 1.474, 1.49, 1.503, 1.52, 1.522, 1.524, 1.551, 
       1.551, 1.609, 1.632, 1.632, 1.676, 1.684, 1.685, 1.728, 1.74, 
       1.761, 1.764, 1.785, 1.804, 1.816, 1.824, 1.836, 1.879, 1.883, 
       1.892, 1.898, 1.934, 1.947, 1.976, 2.02, 2.023, 2.05, 2.059, 
       2.068, 2.071, 2.098, 2.13, 2.204, 2.317, 2.334, 2.34, 2.346, 
       2.378, 2.483, 2.269)

mod4 <- gamlss(y~1, family=NEE)

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod4, what="mu"))
exp(coef(mod4, what="sigma"))

hist(y, freq=FALSE)
curve(dNEE(x, mu=2.400515, sigma=25.15236), 
      add=TRUE, col="tomato", lwd=2)

# Empirical cdf and estimated ecdf
plot(ecdf(y))
curve(pNEE(x, mu=2.400515, sigma=25.15236), 
      add=TRUE, col="tomato", lwd=2)
# QQplot
qqplot(y, rNEE(n=length(y), mu=2.400515, sigma=25.15236), col="tomato")
qqline(y, distribution=function(p) qNEE(p, mu=2.400515, sigma=25.15236))

# Example 5 -------------------------------------------------------------------
# 69 Observations of the gauge lengths of 20m.
y <- c(1.312,1.314,1.479,1.552,1.700,1.803,1.861,1.865,1.944,1.958,1.966,1.997,
       2.006,2.021,2.027,2.055, 2.063,2.098,2.140,2.179,2.224,2.240,2.253,2.270,
       2.272,2.274,2.301,2.301,2.359,2.382,2.382,2.426, 2.434,2.435,2.478,2.490,
       2.511,2.514,2.535,2.554,2.566,2.570,2.586,2.629,2.633,2.642,2.648,2.684,
       2.697,2.726,2.770,2.773,2.800,2.809,2.818,2.821,2.848,2.880,2.954,3.012,
       3.067,3.084,3.090,3.096, 3.128,3.233,3.433,3.585,3.585)

mod5 <- gamlss(y~1, sigma.fo=~1, family = NEE)

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod5, what="mu"))
exp(coef(mod5, what="sigma"))

hist(y, freq=FALSE)
curve(dNEE(x, mu=2.197771, sigma=100.8888), add=TRUE, 
      col="tomato", lwd=2)
# Empirical cdf and estimated ecdf
plot(ecdf(y))
curve(pNEE(x, mu=2.197771, sigma=100.8888), add=TRUE, 
      col="tomato", lwd=2)
# QQplot
qqplot(y, rNEE(n=length(y), mu=2.197771, sigma=100.8888), col="tomato")
qqline(y, distribution=function(p) qNEE(p, mu=2.197771, sigma=100.8888))

ousuga/RelDists documentation built on July 4, 2025, 10:55 a.m.