Logistic Distribution Formula

The probability is a measure of certainty that an event might occur. The logistic distribution is a continuous probability distribution which resembles normal distribution. The value of given sample will be equal to the value of the random variable in the probability density function. The cumulative density function is the probability that a random variable takes a smaller value. The below logistic distribution formula is provided to calculate pdf, lower and upper cdf.


E = e- ((x - a) / b)
p = E / (b x (1 + E)2)
lcdf = 1 / (1 + E)
ucdf = 1- lcdf


E = Exponent Value
x = Percentile
a = Location Parameter
b = Scale Parameter
p = Probability Density Function (pdf)
lcdf = Lower Cumulative Density Function (lcdf)
ucdf = Upper Cumulative Density Function (ucdf)

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The distribution function is used in growth models and logistic regression. Find the probability density function, upper cdf and lower cdf using the logistic distribution formula.

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