Difference between gaussian and log-normal distribution

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I have a random variable say X that is a Gaussian distributed with mean equal to zero dB. When I convert it into linear domain, i.e from dB to linear, does it imply that the resulting variable is log-normally distributed?And if yes, would the mean of resulting log-normally distributed variable also be zero? I would be thankful if anyone clears my doubt.

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Yes, the resulting distribution has a log-normal distribution. If $X$ is normally distributed, then $e^X$ has a log-normal distribution. Be careful however, your transformation is not just $\exp$, it must be $10^X$ or something like that, according to the definition of dB.

No, the mean of the resulting variable is not zero. It can't be zero as a log-normally distributed random variable is almost surely positive. However it's possible to determine its mean as a function of the parameters of the original gaussian distribution. See https://en.wikipedia.org/wiki/Log-normal_distribution