(Basic Statistics for Citizen Data Scientist)
The pdf of the Logistic distribution at location parameter µ and scale parameter β is
where β > 0. The cdf is
The inverse of the logistic distribution is
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.
Figure 1 – Statistical properties of the Logistic distribution
Figure 2 shows a graph of the Logistic distribution for different values of μ and β.
Figure 2 – Chart of Logistic distribution
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
Statistics for Beginners in Excel – Logistic Distribution
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