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Old 16th May 2020, 05:04 AM   #1
sphenisc
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Lognormal question

Is the derivative of a lognormal distribution lognormal?

Thanks
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Old 16th May 2020, 09:02 AM   #2
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Just from a visual inspection:

The derivative would start at 0
climb to a peak as the log-normal climbs
fall to 0 as the log-normal peaks.
continue falling below 0 as the log-normal descends
reach a negative peak as the log-normal flattens
and finally approach 0 asymptotically

Doesn't look log-normal to me.
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Old 16th May 2020, 09:18 AM   #3
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Cheers
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Old 16th May 2020, 11:08 AM   #4
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Probability "distribution" function is ambiguous (see Wikipedia).

In my experience it usually refers to the cumulative distribution function, the derivative of which (for a continuous distribution) would be the probability density function.
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Old 17th May 2020, 10:41 AM   #5
sphenisc
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Originally Posted by KAJ View Post
Probability "distribution" function is ambiguous (see Wikipedia).

In my experience it usually refers to the cumulative distribution function, the derivative of which (for a continuous distribution) would be the probability density function.
Thanks, was thinking of the density function, as GodMark2 described
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Old 18th May 2020, 11:52 AM   #6
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Or even simpler: a log-normal distribution has at least some downward-sloping parts, therefor its derivative is sometimes negative, yet a log-normal distribution can only take positive values, hence its derivative is not log-normal.
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