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The shape of the mean residual life function, of GGD can be obtained by solving the natural log likelihood equation using R software (Package Stat 4).
In this section, the applications and goodness of fit of the GLD have been discussed for several lifetime data from biomedical science and engineering and the fit is compared GGD.
The expressions for survival function, hazard rate function and mean residual life function have been obtained.
The goodness of fit of GLD has been compared with the goodness of fit obtained by GGD and found that GLD does not give satisfactory fit in all data sets.
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In order to compare the goodness of fit of GLD and GGD, values of −2ln L , K-S Statistics ( Kolmogorov-Smirnov Statistics) and p-values for the above data sets have been computed and presented in Table 1.
The formulae for computing K-S Statistics are as follows: = the sample size and is the empirical distribution function.
The expressions for the hazard rate function and the mean residual life function of the distribution have been obtained.
Data set 5 This data set is the strength data of glass of the aircraft window reported by .
Data set 6 The following data represent the tensile strength, measured in GPa, of 69 carbon fibers tested under tension at gauge lengths of 20 mm .
It can be easily verified that the gamma distribution, the Lindley (1958) distribution and the exponential distribution are particular cases of (1.1) for (β = 0) , (α = β =1) and(α =1,β = 0) , respectively. have detailed study about various properties of Lindley distribution, estimation of parameter and application for modeling waiting time data in a bank.
Detailed and comparative study on modeling of lifetime data using one parameter Lindley and exponential distributions . (1.1) can be easily expressed as a twocomponent mixture of gamma (α ,θ ) and gamma (α 1,θ ) distributions.
The hazard (or failure) rate function, ) of the GLD is difficult to study because it includes the upper incomplete gamma function.