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Mathematical SETI

Part of the series Springer Praxis Books pp 155-184

Date:

Life-span modeling by finite b-lognormals

  • Claudio MacconeAffiliated withInternational Academy of Astronautics and Istituto Nazionale di Astrofisica Email author 

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Abstract

It is well known that the probability density function(pdf) \( f_{aX+b} (x) \)of the random variable \( {aX+b}\)where a and b are arbitrary real constants with respect to the independent variable x, is related to the pdf \( f_{\rm{X}}(x)\)of the random variable X by the linear transformation formula for random variables that reads:
$$ f_{aX+b}(x)=\frac{1}{\mid a \mid} f_X \left(\frac{x-b}{\mid a \mid}\right).$$
(5.1)