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The purpose of this paper is to develop a monitoring multiple-stream processes control chart with a finite mixture of probability distributions in the manufacture industry.

Data were collected during production of a wheat-based dough in a food industry and the control charts were developed with these steps: to collect the master sample from different production batches; to verify, by graphical methods, the quantity and the characterization of the number of mixing probability distributions in the production batch; to adjust the theoretical model of probability distribution of each subpopulation in the production batch; to make a statistical model considering the mixture distribution of probability and assuming that the statistical parameters are unknown; to determine control limits; and to compare the mixture chart with traditional control chart.

A graph was developed for monitoring a multi-stream process composed by some parameters considered in its calculation with similar efficiency to the traditional control chart.

The control chart can be an efficient tool for customers that receive product batches continuously from a supplier and need to monitor statistically the critical quality parameters.

We provide a Bayesian inference for a mixture of two Pareto distributions which is then used to approximate the upper tail of a wage distribution. The model is applied to the data from the CPS Outgoing Rotation Group to analyze the recent structure of top wages in the United States from 1992 through 2009. We find an enormous earnings inequality between the very highest wage earners (the “superstars”), and the other high wage earners. These findings are largely in accordance with the alternative explanations combining the model of superstars and the model of tournaments in hierarchical organization structure. The approach can be used to analyze the recent pay gaps among top executives in large firms so as to exhibit the “superstar” effect.

The purpose of this paper is to address some of the fundamental issues surrounding crop insurance ratemaking, from the perspective of the reinsurer, through the development of a scientific pricing framework.

The generating process of the historical loss cost ratio's (LCR's) are reviewed, and the Erlang mixture distribution is proposed. A modified credibility approach is developed based on the Erlang mixture distribution and the liability weighted LCR, and information from the observed data of the individual region/province is integrated with the collective experience of the entire crop reinsurance program in Canada.

A comprehensive data set representing the entire crop insurance sector in Canada is used to show that the Erlang mixture distribution captures the tails of the data more accurately compared to conventional distributions. Further, the heterogeneous credibility premium based on the liability weighted LCR's is more conservative, and provides a more scientific approach to enhance the reinsurance pricing.

Credibility models are in the early stages of application in the area of agriculture insurance, therefore, the credibility models presented in this paper could be verified with data from other geographical regions.

The credibility-based Erlang mixture model proposed in this paper should be useful for crop insurers and reinsurers to enhance their ratemaking frameworks.

This is the first paper to introduce the Erlang mixture model in the context of agricultural risk modeling. Two modified versions of the Bühlmann-Straub credibility model are also presented based on the liability weighted LCR to enhance the reinsurance pricing framework.

This study aims to estimate the firm size distributions that belong to the service sector and manufacturing sector in Korea.

When estimating the firm size distribution, the author considers the following two major factors. First, the firm size distribution can have a gamma distribution rather than traditional accepted distributions such as Pareto distribution or log-normal distribution. In particular, industry-specific enterprises can have different size distributions of the type of gamma distribution. Second, the firm size distribution that is applied to this study’s data set should reflect a number of factors. For example, estimating mixture gamma distribution for firm size distribution should be required and compared, because the total amount of configuration data is composed of small businesses, medium-sized and large companies.

Using 8,230 number of firm data in 2013, the author estimates mixture gamma distribution for the firm size.

From the comparison, empirical results are found for the following characteristics of core firm size distribution: first, the firm size distribution of the manufacturing sector has a longer tail than firm size distribution of the service sector. Second, the manufacturing firm size distribution dominates the entire country firm size distribution. Third, one factor among the three factors that make up the mixed gamma firm size distribution is described for 99 per cent of the firm size distributions. From the estimated firm size distributions of the service sector and manufacturing sector in Korea, the author simply implies the strategy and policy implications for the start-up firm.

The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented.

First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components.

The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order.

Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.

Prospect theory is now widely accepted as the dominant model of choice under risk, but has not been fully incorporated into applied research because of uncertainty about how to include population-level parameter estimates. The purpose of this paper is to characterize heterogeneity across people to lay a foundation for future applied research.

The paper uses elicitation data from field experiments in Vietnam to fit a finite Gaussian mixture model using the expectation maximization algorithm. Applied results are simulated for investment allocations under myopic loss aversion.

The authors find that about 20 percent of the sample is classified as extremely loss averse, while the rest of the population is only mildly loss averse. This implies a bimodal distribution of loss aversion in the population.

The data set is only moderately sized: 181 subjects. Future research will be needed to extend these results out of sample, and to other regions.

This paper provides empirical evidence that heterogeneity matters in prospect theory modeling. It highlights how policy makers might be misled by assuming that average prospect theory parameters are typical within the population.

The purpose of this paper is to bring out the development of a flexible model for nonstationary crop yield distributions and its applications to decision-making in crop insurance.

The authors design a nonparametric Bayesian approach based on Gaussian process regressions to model crop yields over time. Further flexibility is obtained via Bayesian model averaging that results in mixed Gaussian processes.

Simulation results on crop insurance premium rates show that the proposed method compares favorably with conventional estimators, especially when the underlying distributions are nonstationary.

Unlike conventional two-stage estimation, the proposed method models nonstationary crop yields in a single stage. The authors further adopt a decision theoretic framework in its empirical application and demonstrate that insurance companies can use the proposed method to effectively identify profitable policies under symmetric or asymmetric loss functions.

The normal error distribution for the observations and log-volatilities in a stochastic volatility (SV) model is replaced by the Student-t distribution for robustness consideration. The model is then called the t-t SV model throughout this paper. The objectives of the paper are twofold. First, we introduce the scale mixtures of uniform (SMU) and the scale mixtures of normal (SMN) representations to the Student-t density and show that the setup of a Gibbs sampler for the t-t SV model can be simplified. For example, the full conditional distribution of the log-volatilities has a truncated normal distribution that enables an efficient Gibbs sampling algorithm. These representations also provide a means for outlier diagnostics. Second, we consider the so-called t SV model with leverage where the observations and log-volatilities follow a bivariate t distribution. Returns on exchange rates of Australian dollar to 10 major currencies are fitted by the t-t SV model and the t SV model with leverage, respectively.

This paper aims to investigate a probabilistic mixture model for the nonrigid point set registration problem in the computer vision tasks. The equations to estimate the mixture model parameters and the constraint items are derived simultaneously in the proposed strategy.

The problem of point set registration is expressed as Laplace mixture model (LMM) instead of Gaussian mixture model. Three constraint items, namely, distance, the transformation and the correspondence, are introduced to improve the accuracy. The expectation-maximization (EM) algorithm is used to optimize the objection function and the transformation matrix and correspondence matrix are given concurrently.

Although amounts of the researchers study the nonrigid registration problem, the LMM is not considered for most of them. The nonrigid registration problem is considered in the LMM with the constraint items in this paper. Three experiments are performed to verify the effectiveness and robustness and demonstrate the validity.

The novel method to solve the nonrigid point set registration problem in the presence of the constraint items with EM algorithm is put forward in this work.

This chapter studies trends in income distributions and inequality in the European Union using data from the European Union Statistics on Income and Living Conditions. The author models the income distribution for each country under a Dagum distribution assumption and using maximum likelihood techniques. The author uses parameter estimates to form distributions for regions defined as finite mixtures of the country distributions. Specifically, the author studies the groups of ‘new’ and ‘old’ countries depending on the year they joined the European Union. The author provides formulae and estimates for the regional Gini coefficients and Lorenz curves and their decomposition for all the survey years from 2007 through 2011. The estimates of this study show that the ‘new’ European Union countries have become richer and less unequal over the observed years, while the ‘old’ ones have undergone a slight increase in inequality which is however not significant at conventional levels.