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To complete a previous work, the probability density functions for the errorsin the center-of-gravity as positioning algorithm are derived with the usualmethods of the cumulative distribution functions. These methods introducesubstantial complications compared to the approaches used in a previouspublication on similar problems. The combinations of random variablesconsidered are: $X_{g3}=\theta(x_2-x_1) (x_1-x_3)/(x_1+x_2+x_3) +\theta(x_1-x_2)(x_1+2x_4)/(x_1+x_2+x_4)$ and$X_{g4}=(\theta(x_4-x_5)(2x_4+x_1-x_3)/(x_1+x_2+x_3+x_4)+\theta(x_5-x_4)(x_1-x_3-2x_5)/(x_1+x_2+x_3+x_5)$ The complete and partial formsof the probability density functions of these expressions of thecenter-of-gravity algorithms are calculated for general probability densityfunctions of the observation noise. The cumulative probability distributionsare the essential steps in this study, never calculated elsewhere.

Positioning Error Probabilities for Some Forms of Center-of-Gravity Algorithm Calculated with the Cumulative Distributions. Part II