Logistic 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))))

 

where:

• 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).