A Note on α-Curvature of the Manifolds of the Length-biased Lognormal and Gamma Distributions in View of Related Applications in Data Analysis

Abstract

The α-curvature tensors of the statistical manifolds of the length-biased versions of the log-normal and gamma distributions are derived and discussed. This study was designed to investigate observations related to the parameter estimation for the length-biased lognormal distribution as a model for the lengthbiased data from oil field exploration.