An apparatus for analysing the condition of a machine having a part rotating with a speed of rotation (f ROT), the rotating part including a bearing having a bearing surface; the apparatus comprising: means for receiving a first digital signal (S RED, S MD, S ENV) dependent on mechanical vibrations emanating from rotation of said part; and data processing means coupled to a memory, the data processing means and memory being configured for: analysing said first digital signal (S RED, S MD, S ENV) so as to detect peak amplitude values (Ap) during a finite time period (Pm), said finite time period corresponding to a certain amount (R; n ∗ R) of revolution of said rotating part; said certain amount (R; n ∗ R) of revolution corresponding to more than one revolution of said rotating part; and sorting said detected peak amplitude values (Ap) into a plurality (N R) of corresponding amplitude ranges so as to reflect occurrence of detected peak amplitude values (Ap) within said plurality of amplitude ranges; the apparatus being characterized in that the data processing means and memory are further configured for estimating, in dependence on said sorted peak amplitude values (Ap) and said certain amount (R; n ∗ R), a not-so-frequent representative peak amplitude value (A PR, 590) indicative of a mechanical state of said bearing surface and are further configured for estimating said not-so-frequent representative peak amplitude value (A PR, 590) based on the nature of the Gaussian function or bell curve being such that amplitude and occurrence frequency of low amplitude values (550, 560) are informative about the amplitude of the not-so-frequent representative peak amplitude value (A PR, 590); the apparatus being further characterized in that the data processing means and memory are configured to use said sorted peak amplitude values (Ap, r g, r h, 550) having an average occurrence frequency of one per revolution (g), and/or less than one per revolution (h) for estimating said not-so-frequent representative_value (A PR, 590) having an average occurrence frequency of one per eight revolutions or less than one per eight revolutions; wherein said sorted peak amplitude values (Ap, r g, r h, 550) being used for said estimation step have an average occurrence frequency (g, h) of more than one per eight revolutions. means for receiving a first digital signal (S RED, S MD, S ENV) dependent on mechanical vibrations emanating from rotation of said part; and data processing means coupled to a memory, the data processing means and memory being configured for: analysing said first digital signal (S RED, S MD, S ENV) so as to detect peak amplitude values (Ap) during a finite time period (Pm), said finite time period corresponding to a certain amount (R; n ∗ R) of revolution of said rotating part; said certain amount (R; n ∗ R) of revolution corresponding to more than one revolution of said rotating part; and sorting said detected peak amplitude values (Ap) into a plurality (N R) of corresponding amplitude ranges so as to reflect occurrence of detected peak amplitude values (Ap) within said plurality of amplitude ranges; the apparatus being characterized in that the data processing means and memory are further configured for estimating, in dependence on said sorted peak amplitude values (Ap) and said certain amount (R; n ∗ R), a not-so-frequent representative peak amplitude value (A PR, 590) indicative of a mechanical state of said bearing surface and are further configured for estimating said not-so-frequent representative peak amplitude value (A PR, 590) based on the nature of the Gaussian function or bell curve being such that amplitude and occurrence frequency of low amplitude values (550, 560) are informative about the amplitude of the not-so-frequent representative peak amplitude value (A PR, 590); the apparatus being further characterized in that the data processing means and memory are configured to use said sorted peak amplitude values (Ap, r g, r h, 550) having an average occurrence frequency of one per revolution (g), and/or less than one per revolution (h) for estimating said not-so-frequent representative_value (A PR, 590) having an average occurrence frequency of one per eight revolutions or less than one per eight revolutions; wherein said sorted peak amplitude values (Ap, r g, r h, 550) being used for said estimation step have an average occurrence frequency (g, h) of more than one per eight revolutions.