The representation of the entropy in terms of the hazard function and its extensions have been studied by many authors including Teitler et al. (IEEE Trans Reliab 35:391–395, <CitationRef CitationID="CR16">1986</CitationRef>). In this paper, we consider a representation of the Kullback–Leibler information of the first <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$r$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>r</mi> </math> </EquationSource> </InlineEquation>...</equationsource></equationsource></inlineequation></citationref>

In this work the ranked set sampling technique has been applied to estimate the scale parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> </InlineEquation> of a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in...</equationsource></inlineequation>