Counting Death to Measure Survival: An Analytic Technique of Measuring Mortality Rate Intensity from the Heligman-Pollard’s Law

Abstract

The Heligman-Pollard model is distinguished to be one of the most influential multi-component parsimonious laws of mortality incorporating age-specific mortality trends with interpretable framework. However, the complexity of its form, computation challenges and lack of mechanistic grounding being overlooked in actuarial literature serve as the motivation in addressing it more as an analytic law. The objectives are to generate mortality table, derive the probability of survival function and test its asymptotic properties, and state the structural properties of the law. Computational evidence from our results reveals that for both sexes, the second component exhibits lognormal kernel expressed as the accidental hump into higher adulthood within the age interval  for both sexes. Consequently, the lognormal behaviour caused its trajectories to exhibit leptokurtic curves which described the shape of the mortality distribution in the second terms. The implication is that the leptokurtic mortality distribution has a higher number of intensities clustered around the mean deaths with more extreme severities in the tails relative to a normal distribution.