Abstract
Here we consider a generalized log-transformed version of the Weibull distribution and investigate some of its important properties like expressions for the cumulative distribution function hazard rate function, quantile function, characteristic function, raw moments, incomplete moments, etc. The distribution and moments of order statistics are obtained along with some results on certain structural properties of the distribution. The maximum likelihood estimation of the parameters of the distribution is attempted for both complete and censored data sets and the usefulness of the distribution is illustrated with the help of real-life data sets from biomedical fields.
Highlights
The generalized versions of Weibull distribution (WD) and their applications have gained much importance in fields of engineering, ecology, medicine, pharmacy, etc. due to the flexibility of these distributions in handling survival data
The plots of the p.d.f., the c.d.f. and the hazard rate function of the generalized log-Weibull distribution (GLWD)(α, β) for particular values of its parameters are presented in Figures 1, 2, and 3
We present certain series representations and integrals which we require in the sequel for deriving expressions for the characteristic function and moments of the GLWD(α, β)
Summary
The generalized versions of Weibull distribution (WD) and their applications have gained much importance in fields of engineering, ecology, medicine, pharmacy, etc. due to the flexibility of these distributions in handling survival data. E-ISSN: 1929-6029/21 function including most of the monotone as well as non-monotone hazard rate shapes such as increasing, decreasing, bathtub, upside-down bathtub, and ‘S’ shapes and is more flexible in terms of its measures of central tendency, dispersion, skewness, and kurtosis, which highlights the utility of the model as a lifetime distribution. As such the proposed distribution can be considered to be a better alternative for many of the recently developed modifications of the WD.
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