 The cumulative distribution function (cdf) of the half-logistic distribution is intimately related to the cdf of the logistic distribution.Formally, if "F"("k") is the cdf for the logistic distribution, then "G"("k") = 2"F"("k") − 1 is the cdf of a half-logistic distribution.Specifically,

Similarly, the probability density function (pdf) of the half-logistic distribution is "g"("k") = 2"f"("k") if "f"("k") is the pdf of the logistic distribution.