The logistic distribution is a sigmoid shaped curve showing the cumulative percentage as one proceeds along the normal distribution.


If a value is known, its position in the normal distribution can be calculated using the following equation.


F(value) =

= 1 / (1 + EXP((-1) * 1.8138 * (((value) – (distribution mean)) / (standard deviation))))



• 1.8138 = PI / SQRT(3)


The inverse function can be used to determine the value of X that is located at a given decimal fraction (from 0 to 1.00) along the distribution:


X =

= (distribution mean) – ((standard deviation) / 1.8138) * LN((1-(decimal fraction)) / (decimal fraction)))


These equations can be used in genetics to predict the age of onset for a given penetrance (see chapter on genetics, under: logistic distribution curve for age of onset).


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