Related Experiment Video
Updated: Aug 15, 2026

Measurement of Lifespan in Drosophila melanogaster
Published on: January 7, 2013
Bounds on life expectancy for the Rayleigh and Weibull distributions
Abstract:
Bounds are presented for the life expectancy or the mean residual life of an individual whose lifetime is a random variable X following a Rayleigh distribution or more generally a Weibull distribution. Simple transformations of the variables give inequalities on the Mills' ratio and the incomplete gamma functions. Some numerical computations are also reported to compare the lower and upper bounds with the exact value of the life expectancy function for several values of the parameter. When the lifetime follows a Gompertz distribution, the problem becomes complicated, and it has not been possible to construct bounds on the life expectancy function. The importance of the Gompertz distribution in the dynamics of normal and tumor growth and in the embryonic and postnatal growth of birds and mammals is demonstrated, and life expectancy is evaluated by numerical methods for a number of parameter values.
Related Concept Videos
Life Tables
Survival Curves
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...
Actuarial Approach
Consider the example of a high-risk surgical procedure with significant early-stage mortality. A two-year clinical study is conducted,...
Kaplan-Meier Approach
Applications of Life Tables
Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

