Logistic Distribution

Properties

The pdf of the Logistic distribution at location parameter µ and scale parameter β is

logistic distribution pdf

where β > 0. The cdf is

logistic distribution cdf

The inverse of the logistic distribution is

logistic distribution inverse function

The standard Gumbel distribution is the case where μ = 0 and β = 1.

Key statistical properties of the Logistic distribution are shown in Figure 1.

Logistic distribution propertiesFigure 1 – Statistical properties of the Logistic distribution

Graphs

Figure 2 shows a graph of the Logistic distribution for different values of μ and β.

Logistic distribution chart

Figure 2 – Chart of Logistic distribution

Worksheet Functions

Real Statistics Functions: The Real Statistics Resource Pack provides the following functions for the Logistic distribution.

LOGISTIC_DIST(x, μ, β, cum) = the pdf of the Logistic distribution f(x) when cum = FALSE and the corresponding cumulative distribution function F(x) when cum = TRUE.

LOGISTIC_INV(p, μ, β) = the inverse of the Logistic distribution at p

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Wikipedia (2020) Logistic distribution
https://en.wikipedia.org/wiki/Logistic_distribution

Hastings, N., Peacock, B. (2011) Statistical distributions. 4th Ed, Wiley
https://www.wiley.com/en-us/Statistical+Distributions%2C+4th+Edition-p-9780470390634

2 thoughts on “Logistic Distribution”

  1. After downloading the resource pack on my android, I am still getting an error for using the function LOGISTIC_DIST. I believe this particular function is still not supported by the downloaded version.

    Reply
    • Hello Adebayo,
      I just checked and LOGISTIC_DIST works on my computer.
      You say that you downloaded the Real Statistics Resource Pack on your android. Did you also install the resource pack? I ask since I don’t think the resource pack works on android. What do you see when you enter the formula =VER() in any cell?
      Charles

      Reply

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