Gompertz hazard modeling shows exponential increase in age-specific mortality. Parameter α sets initial mortality rate, while β represents exponential senescence acceleration.
The question "What are you starting to like more as you get older?" involves three distinct statistical components:
This explains the saved simulation equations, not personal mortality estimates or measured age preferences. Hazard is alpha times exponential beta times age, plus gamma. Survival is the exponential of the negative cumulative hazard: alpha divided by beta times exponential beta age minus one, plus gamma times age. For illustrative cumulative hazards equal to the logarithm of two and the logarithm of four, survival is one half and one quarter. At six hundred pixels per survival probability unit the bars span three hundred and one hundred fifty pixels. These are formula examples, not observed cohort fractions. The plotted survival curve integrates from age zero, while the agent simulator initializes every agent alive at its current age, initially twenty. Its live survivor fraction therefore does not start as a sample of the plotted unconditional age-zero survival curve. Each simulation step uses the current hazard to calculate one minus exponential negative hazard times time step. For hypothetical hazard point one and step one, death probability is approximately point zero nine five one six three. Doubling hazard to point two gives approximately point one eight one two six nine, not exactly twice the first probability. Bars at fifteen hundred pixels per probability unit span about one hundred forty two point seven four and two hundred seventy one point nine pixels. A random draw is made for each living agent; dead agents remain dead. The rule freezes hazard over that step rather than integrating changing hazard throughout the interval. Finite random cohorts need not equal the analytical probability at every step. All coefficients in this saved simulation are assumed inputs rather than fitted demographic evidence. Only surviving agents update preference toward a target equal to point one plus age divided by one hundred times point eight five, capped at point nine five. At age fifty the target is point five two five. Starting from point two, with drift point zero three five and step one, the new preference is point two one one three seven five. Bars at two thousand pixels per preference unit span four hundred and four hundred twenty two point seven five pixels. The displayed mean averages living agents and returns zero when none remain. CSV instead exports one hundred one analytical age rows from zero through one hundred, with survival, hazard and the target preference curve. It does not export the random agent history or the mean of actual survivors. Offline p five is unavailable before chart initialization and event binding. Matching that original failure does not prove healthy simulation controls.