Estimating Income Inequality in China Using Grouped Data and the Generalized Beta Distribution

There are two main types of data sources of income distributions in China: household survey data and grouped data. Household survey data are typically available for isolated years and individual provinces. In comparison, aggregate or grouped data are typically available more frequently and usually have national coverage. In principle, grouped data allow investigation of the change of inequality over longer, continuous periods of time, and the identification of patterns of inequality across broader regions. Nevertheless, a major limitation of grouped data is that only mean (average) income and income shares of quintile or decile groups of the population are reported. Directly using grouped data reported in this format is equivalent to assuming that all individuals in a quintile or decile group have the same income. This potentially distorts the estimate of inequality within each region. The aim of this paper is to apply an improved econometric method designed to use grouped data to study income inequality in China. A generalized beta distribution is employed to model income inequality in China at various levels and periods of time. The generalized beta distribution is more general and flexible than the lognormal distribution that has been used in past research, and also relaxes the assumption of a uniform distribution of income within quintile and decile groups of populations. The paper studies the nature and extent of inequality in rural and urban China over the period 1978 to 2002. Income inequality in the whole of China is then modeled using a mixture of province-specific distributions. The estimated results are used to study the trends in national inequality, and to discuss the empirical findings in the light of economic reforms, regional policies, and globalization of the Chinese economy.

Recoverable reserves and support effects when optimizing open pit mine designs

Orebody modelling, support effects and the estimation of recoverable reserves are key parts of open pit optimization studies. A case study is presented on the estimation of recoverable reserves using an implementation of indicator kriging where metal quantity is used to select cutoffs, and support corrections founded on a conditional simulation approach. Mining selectivity is explored in the subsequent optimization study to compare results from indicator kriging of grade estimates on a regular size blocks and indicator kriging estimates on small size blocks. The use of indicator kriging models adjusted for a given selectivity and the use of grade proportions in each block for the optimization study, provide a presentation of the expected ore recovery for a predefined level of selectivity. The case study shows that indicator kriging estimation with full accounting of block grade distributions generates substantially better results in the pit optimization study. In addition, the adverse effects of small blocks and over-smoothing on optimization results are illustrated.

Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Prospective evaluation of a D-optimal designed population pharmacokinetic study

Recently, methods for computing D-optimal designs for population pharmacokinetic studies have become available. However there are few publications that have prospectively evaluated the benefits of D-optimality in population or single-subject settings. This study compared a population optimal design with an empirical design for estimating the base pharmacokinetic model for enoxaparin in a stratified randomized setting. The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB version 6.0.0.88). The optimal design was based on a one-compartment model with lognormal between subject variability and proportional residual variability and consisted of a single design with three sampling windows (0-30 min, 1.5-5 hr and 11 - 12 hr post-dose) for all patients. The empirical design consisted of three sample time windows per patient from a total of nine windows that collectively represented the entire dose interval. Each patient was assigned to have one blood sample taken from three different windows. Windows for blood sampling times were also provided for the optimal design. Ninety six patients were recruited into the study who were currently receiving enoxaparin therapy. Patients were randomly assigned to either the optimal or empirical sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded. Analysis was undertaken using NONMEM (version 5). The empirical design supported a one compartment linear model with additive residual error, while the optimal design supported a two compartment linear model with additive residual error as did the model derived from the full data set. A posterior predictive check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This revealed the optimal'' design derived model was superior to the empirical design model in terms of precision and was similar to the model developed from the full dataset. This study suggests optimal design techniques may be useful, even when the optimized design was based on a model that was misspecified in terms of the structural and statistical models and when the implementation of the optimal designed study deviated from the nominal design.

Successive nonparametric estimation of conditional distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities.

Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?

In cell lifespan studies the exponential nature of cell survival curves is often interpreted as showing the rate of death is independent of the age of the cells within the population. Here we present an alternative model where cells that die are replaced and the age and lifespan of the population pool is monitored until a, steady state is reached. In our model newly generated individual cells are given a determined lifespan drawn from a number of known distributions including the lognormal, which is frequently found in nature. For lognormal lifespans the analytic steady-state survival curve obtained can be well-fit by a single or double exponential, depending on the mean and standard deviation. Thus, experimental evidence for exponential lifespans of one and/or two populations cannot be taken as definitive evidence for time and age independence of cell survival. A related model for a dividing population in steady state is also developed. We propose that the common adoption of age-independent, constant rates of change in biological modelling may be responsible for significant errors, both of interpretation and of mathematical deduction. We suggest that additional mathematical and experimental methods must be used to resolve the relationship between time and behavioural changes by cells that are predominantly unsynchronized.