The properties of non-parametric kernel estimators for probability density function from two special classes are investigated. Each class is parametrized with distribution smoothness parameter. One the was introduced by Rosenblatt, another one in this paper. For case known parameter, rates mean square convergence optimal (on bandwidth) found. unknown estimation procedure parameter developed and...

Starting from a stochastic agent-based model to represent market exchange in a developing economy, we study time variations of the probability density function of income with simultaneous variation of the consumption deprivation (CD), where CD represents the shortfall in consumption from the saturation level of an essential commodity, cereal. Together, these two models combine income-expenditur...