Logistic Distribution Percent Point Calculator

Find the percent point (quantile) of the logistic distribution from a probability p with location μ and scale s using the logit transform.

Input

Find the percent point (quantile) of the logistic distribution. Enter a probability p with location μ and scale s.

Probability p

A value strictly between 0 and 1

Probability type

Whether p is a lower tail or upper tail probability

Location μ

Center of the distribution (any real number)

Scale s

A positive value controlling the spread

Percent point x for lower probability 0.95

2.94443898

Location μ

Scale s

Mean

Variance

3.28986813

Lower probability F(x)

0.95

Upper probability 1 − F(x)

0.05

Density f(x)

0.0475

Probability density function (PDF)

Cumulative distribution function (CDF)

The cumulative distribution of the logistic distribution is F(x) = 1 / (1 + e^(−z)) with z = (x − μ) / s, which is the logistic (sigmoid) function.
For a lower probability p the percent point follows in closed form from the logit transform as x = μ + s·ln(p/(1−p)). When an upper probability is given, p is replaced by 1 − p.
The probability density is f(x) = e^(−z) / (s·(1 + e^(−z))²) and is symmetric about the location μ. The mean is μ and the variance is (π²/3)·s².
Enter p strictly between 0 and 1 and a positive scale s. As p approaches 0 or 1 the percent point diverges toward minus or plus infinity.

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