A General Algorithm for Estimating a Markov-Generated Increment-Decrement Life Table with Applications to Marital-Status Patterns

Abstract

Extant methods of estimating increment-decrement life tables (IDLT's) are based on the assumption that the forces of transition from state to state are constant within each interval of time (age) examined. A general algorithm for estimating the functions of a (k + 1)-state Markovian IDLT is set forth herein, which treats the constant-forces assumption as a special case. Three different kinds of probabilities, called p π, and χ probabilities, are identified, and their properties are discussed. Particular attention is focused on the three-state case in which the survival functions are assumed to be linear within each age interval, and such a model is applied to the analysis of marital dissolution and remarriage using data for females in Sweden, cohort born 1930–34.

Key Words:

• Markov chains
• Population models
• Marital dissolution and remarriage
• Forces of transition
• Transition probabilities
• Occurrence/exposure rates