A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

Statistical Size Distributions in Economics and Actuarial Sciences

Mendelian randomization (MR) uses genetic data to probe questions of causality in epidemiological research, by invoking the Instrumental Variable (IV) assumptions. In recent years, it has become commonplace to attempt MR analyses by synthesising summary data estimates of genetic association gleaned from large and independent study populations. This is referred to as two-sample summary data MR. Unfortunately, due to the sheer number of variants that can be easily included into summary data MR analyses, it is increasingly likely that some do not meet the IV assumptions due to pleiotropy. There is a pressing need to develop methods that can both detect and correct for pleiotropy, in order to preserve the validity of the MR approach in this context. In this paper, we aim to clarify how established methods of meta-regression and random effects modelling from mainstream meta-analysis are being adapted to perform this task. Specifically, we focus on two contrastin g approaches: the Inverse Variance Weighted (IVW) method which assumes in its simplest form that all genetic variants are valid IVs, and the method of MR-Egger regression that allows all variants to violate the IV assumptions, albeit in a specific way. We investigate the ability of two popular random effects models to provide robustness to pleiotropy under the IVW approach, and propose statistics to quantify the relative goodness-of-fit of the IVW approach over MR-Egger regression. © 2017 The Authors. Statistics in Medicine Published by JohnWiley & Sons Ltd.

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A framework for the investigation of pleiotropy in two-sample summary data Mendelian randomization

Analysis of Binary Data.

Applied Discriminant Analysis

Multivariate Statistical Simulation

The subject of assessing whether a data set is from a speciflc dis- tribution is crucial in statistical inference. This topic is critically important for uniform distributions as in generating random samples, a random sample is taken from the standard uniform distribution and then converted to the sam- ple as required. Two difierent modiflcations of the Anderson-Darling A2 test are presented. The critical values for the modiflcations and the usual A2 test are also re-computed for difierent sample sizes. This is followed by a power comparison of the various tests.

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A modified Anderson-Darling test for uniformity.

Exponential distributions are used extensively in the field of life-testing. Estimation of parameters is revisited in two-parameter exponential distributions. A comparison study between the maximum likelihood method, the unbiased estimates which are linear functions of the maximum likelihood method, the method of product spacings, and the method of quantile estimates are presented. Finally, a simulation study is given to demonstrate the small sample properties

Estimation in two-parameter exponential distributions

A combination of a parametric estimate and a nonparametric estimate of a model for a regression function is considered. The optimal linear combination is estimated from the data by the least squares estimate of the combining coefficient. The estimate so obtained is compared with the one proposed by Wooldridge (1992) and Burman and Chaud-huri,the latter being based on Stein (1956). A test procedure for deciding about the parametric specification is also studied.

A note on combining parametric and non-parametric regression

The Box-Cox transformation is a well known family of power transformations to bring a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. This paper proposes a new method for estimating the Box-Cox transformation using maximization of the Shapiro-Wilk W statistic which forces the data to get closer to normal as much as possible. A comparative study of the proposed procedure with the normal based likelihood procedure and the artificial regression model procedure also presented.

Mezbahur Rahman

Papers

A modified Anderson-Darling test for uniformity.

Estimation in two-parameter exponential distributions

A note on combining parametric and non-parametric regression

Estimating the box-cox transformation via shapiro-wilk W Statistic

Improved Combined Parametric and Nonparametric Regressions: Estimation and Hypothesis Testing