Logistic Probability Distribution
Invert a logistic CDF and compare location, scale and the distribution’s actual variance.
Free theory articleInvert a logistic CDF and compare location, scale and the distribution’s actual variance.
Concept & interpretation
The Logistic distribution is a continuous probability distribution often used in logistic regression and feedforward neural networks. While it resembles the Normal distribution in shape, it has heavier tails (higher kurtosis). This module demonstrates how to invert a logistic CDF and compares its location, scale, and actual variance.
experiment
You can interactively explore the logistic distribution by adjusting its location, scale, and observing probe/quantile results in the Logistic Probability Distribution module.
- Change the Location control to shift the distribution left or right along the x-axis. Notice how the Mean matches the Location directly.
- Adjust the Scale control. A larger scale flattens the density curve and increases the Variance drastically according to the
s²term. - Change the Probe x control to see how the Density and CDF values change at different points along the distribution.
- Adjust the Quantile probability to see the inverse CDF in action, mapping a target probability back to a coordinate on the x-axis.