Compound Distribution Models of Inter-regional Migration

Abstract

In this study, the probability distribution of migrant population is examined on the basis that inter-regional migration is a combined process of, firstly, the household decision making, and, secondly, the probability distribution of sizes of migrating households. Though in the area of migration studies, the multinomial distribution which is used in the entropy maximizing model is well known, there are many other multivariate discrete probability distributions developed and utilized in mathematical ecology, financial engineering and other fields (Mosimann (1962, 1963), Shibuya & Shimizu (2002), Wang (2000)). Significance of these multivariate discrete probability distributions in the area of the inter-regional migration studies is explored.
Further, on the assumption that the probability distribution of migrant population is a compound distribution of those of migrating households and migrating household sizes, migrating household models based on these multivariate discrete distributions are expanded for examining the characteristics of the distributions of migrating population. Expected values, variances and covariances of the migrant population are derived from the characteristic functions of the compound distributions, and it is found that the variance can be expressed as a quadratic function (without a constant) of the expected value, and that the first-order parameter is closely related to the average size of migrating households.

JEL classification: C16, R23