heuristic function

Heuristic method of estimation

Heuristic method for the estimation of parameters of the discrete inverse Weibull

heuristic(x, beta1=1, z = 0.1, r = 0.1, Leps = 0.01)

Arguments

• x: a vector of sample values
• beta1: launch value of the $\beta$ parameter
• z: initial value of width
• r: initial value of rate
• Leps: tolerance error for the likelihood function

Returns

a list containig the two estimates of $q$ and $\beta$

Details

For a detailed description of the method, have a look at the reference

See Also

estdiweibull

Examples

n<-50
q<-0.25
beta<-1.5
x<-rdiweibull(n, q, beta)
# estimates using the heuristic algorithm
par0<-heuristic(x)
par0
# change the default values of some working parameters...
par1<-heuristic(x, beta1=2)
par1
par2<-heuristic(x, z=0.5)
par2
par3<-heuristic(x, r=0.2)
par3
par4<-heuristic(x, Leps=0.1)
par4
# ...there should be just light differences among the estimates...
# ... and among the corresponding values of the loglikelihood functions
loglikediw(x, par0[1], par0[2])
loglikediw(x, par1[1], par1[2])
loglikediw(x, par2[1], par2[2])
loglikediw(x, par3[1], par3[2])
loglikediw(x, par4[1], par4[2])

References

Jazi M.A., Lai C.-D., Alamatsaz M.H. (2010) A discrete inverse Weibull distribution and estimation of its parameters, Statistical Methodology, 7: 121-132

Drapella A. (1993) Complementary Weibull distribution: unknown or just forgotten, Quality Reliability Engineering International 9: 383-385