The rate of profit as a random variable

This thesis is a systematic attempt to investigate two conjectures about the distribution of company rates of profit: that it should be log-normal (Gibrat 1931), and that it should be gamma distributed (Farjoun and Machover 1983). A large set of company accounts data is analysed, and partial support found for Gibrat and for a generalised version of Farjoun and Machover. The analysis includes a demonstration of different empirical distributions for different profit rate measures, a demonstration of power law tails in all measures of the profit rate, and a demonstration of size effects (differences in tail weights) in financial ratios. Annual variation in the overall skewness and kurtosis of profit rate distributions is shown to be dominated by variation in the power law tails. L-moments, a recent innovation in robust methods to deal with extreme values, are used in conjunction with a size-weighted sampling scheme to identify possible models for distributions of the profit rate at the capital level. Farjoun and Machover derive their hypothesis from a particular conception of the process of capitalist competition. A rival conception, that of Glick (1985), is tested using company accounts data and shown to be vulnerable to criticism concerning the scope of its data set, the test statistic employed, and its choice of profit rate measure. More fundamentally, it is also dependent on doubtful premises about the within-industry distribution of profit rates, as L-moment analysis demonstrates

TREATMENT OF INFLUENTIAL OBSERVATIONS IN THE CURRENT EMPLOYMENT STATISTICS SURVEY

It is common for many establishment surveys that a sample contains a fraction of observations that may seriously affect survey estimates. Influential observations may appear in the sample due to imperfections of the survey design that cannot fully account for the dynamic and heterogeneous nature of the population of businesses. An observation may become influential due to a relatively large survey weight, extreme value, or combination of the weight and value. We propose a Winsorized estimator with a choice of cutoff points that guarantees that the resulting mean squared error is lower than the variance of the original survey weighted estimator. This estimator is based on very un-restrictive modeling assumptions and can be safely used when the sample is sufficiently large. We consider a different approach when the sample is small. Estimation from small samples generally relies on strict model assumptions. Robustness here is understood as insensitivity of an estimator to model misspecification or to appearance of outliers. The proposed approach is a slight modification of the classical linear mixed model application to small area estimation. The underlying distribution of the random error term is a scale mixture of two normal distributions. This setup can describe outliers in individual observations. It is also suitable for a more general situation where units from two distinct populations are put together for estimation. The mixture group indicator is not observed. The probabilities of observations coming from a group with a smaller or larger variance are estimated from the data. These conditional probabilities can serve as the basis for a formal test on outlyingness at the area level. Simulations are carried out to compare several alternative estimators under different scenarios. Performance of the bootstrap method for prediction confidence intervals is investigated using simulations. We also compare the proposed method with alternative existing methods in a study using data from the Current Employment Statistics Survey conducted by the U.S. Bureau of Labor Statistics

Symmetry in Applied Mathematics

Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page