Question: The logistic cumulative distribution function is
F(y) = 1/{1 + exp[- (y - μ)/σ]}, -∞ < y < ∞,
where the scale parameter u is positive and the location parameter p has any value.
(a) Find the relationship between life y and cumulative hazard H.
(b) To make hazard paper, calculate the positions corresponding to cumulative hazards of 1, 2, 5, 10, 20, 50, 100, 200, and 500% on the cumulative hazard scale.
(c) Calculate the positions corresponding to cumulative probabilities of 1, 2, 5, 10, 20, 50, 80, 90, 95, 98, and 99% on the probability scale.
(d) Carefully draw the logistic hazard plotting paper and include the probability scale.
(e) Explain how to use the hazard scale to estimate µ and σ.