Cramer-von Mises Test Statistic Research Articles

The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data

The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided.

Methods of Estimating the Parameters of the Quasi Lindley Distribution

In this paper, we review the quasi Lindley distribution and established its quantile function. A simulation study is conducted to examine the bias and mean square error of the parameter estimates of the distribution through the method of moment estimation and the maximum likelihood estimation. Result obtained shows that the method of maximum likelihood is a better choice of estimation method for the parameters of the quasi Lindley distribution. Finally, an applicability of the quasi Lindley disttribution to a waiting time data set suggests that the distribution demonstrates superiority over the power Lindley distribution, Sushila distribution and the classical oneparameter Lindley distribution in terms of the maximized loglikelihood, the Akaike information criterion, the Kolmogorov-Smirnov and Cramer von Mises test statistic.

Bias in Balance Optimization Subset Selection: Exploration through examples

When estimating a treatment effect from observational data, researchers encounter bias regardless of estimation methods. In this paper, we focus on a particular method of estimation called Balance Optimization Subset Selection (BOSS). This paper investigates all the possible cases that may lead to bias in the context of BOSS, provides examples for those cases and tries to mitigate the bias. While doing so, we define a balance hierarchy and a correct imbalance measure which corresponds to the form of the response functions. In addition, new imbalance measures drawn from the Cramer-von Mises test statistic are introduced. The cases of insufficient data and suboptimality that can arise in causal analysis with BOSS are also presented.

A constructive hypothesis test for the single-index models with two groups

Comparison of two-sample heteroscedastic single-index models, where both the scale and location functions are modeled as single-index models, is studied in this paper. We propose a test for checking the equality of single-index parameters when dimensions of covariates of the two samples are equal. Further, we propose two test statistics based on Kolmogorov–Smirnov and Cramer–von Mises type functionals. These statistics evaluate the difference of the empirical residual processes to test the equality of mean functions of two single-index models. Asymptotic distributions of estimators and test statistics are derived. The Kolmogorov–Smirnov and Cramer–von Mises test statistics can detect local alternatives that converge to the null hypothesis at a parametric convergence rate. To calculate the critical values of Kolmogorov–Smirnov and Cramer–von Mises test statistics, a bootstrap procedure is proposed. Simulation studies and an empirical study demonstrate the performance of the proposed procedures.

On Testing for Independence between Several Time Series

Test statistics for checking the independence between the innovations of several time series are developed. The time series models considered allow for general specifications for the conditional mean and variance functions that could depend on common explanatory variables. In testing for independence between more that two time series, checking pairwise independence does not lead to consistent procedures. Thus a finite family of empirical processes relying on multivariate lagged residuals are constructed, and we derive their asymptotic distributions.In order to obtain simple asymptotic covariance structures, Mobius transformations of the empirical processes are studied, and simplifications occur. Under the null hypothesis of independence, we show that these transformed processes are asymptotically Gaussian, independent, and with tractable covariance functions not depending on the estimated parameters. Various procedures are discussed, including Cramer-von Mises test statistics and tests based on non-parametric measures. The ranks of the residuals are considered in the new methods, giving tests statistics which are asymptotically margin-free. Generalized cross-correlations are introduced, generalizing the concept of cross-correlation to an arbitrarily number of time series; portmanteau procedures based on them are discussed. In order to detect the dependence visually, graphical devices are proposed. Simulations are conducted to explore the finite sample properties of the methodology, which is found to be powerful against various types of alternatives when the independence is tested between two and three time series. An application is considered, using the daily log-returns of Apple, Intel and Hewlett-Packard traded on the Nasdaq financial market.

Impact of microfiltration treatment of secondary wastewater effluent on biofouling of reverse osmosis membranes

The effects of microfiltration (MF) as pretreatment for reverse osmosis (RO) on biofouling of RO membranes were analyzed with secondary wastewater effluents. MF pretreatment reduced permeate flux decline two- to three-fold, while increasing salt rejection. Additionally, the oxygen uptake rate (OUR) in the biofouling layer of the RO membrane was higher for an RO system that received pretreated secondary wastewater effluent compared to a control RO system that received untreated secondary effluent, likely due to the removal of inert particulate/colloidal matter during MF. A higher cell viability in the RO biofilm was observed close to the membrane surface irrespective of pretreatment, which is consistent with the biofilm-enhanced concentration polarization effect. Bacterial 16S rRNA gene clone library analysis revealed dominant biofilm communities of Proteobacteria and Bacteroidetes under all conditions. The Cramer–von Mises test statistic showed that MF pretreatment did not significantly change the bacterial community structure of RO membrane biofilms, though it affected bacterial community structure of non-membrane-associated biofilms (collected from the feed tank wall). The finding that the biofilm community developed on the RO membrane was not influenced by MF pretreatment may imply that RO membranes select for a conserved biofilm community.

Testing for Equality between Two Copulas

We develop a test of equality between two dependence structures estimated through empirical copulas. We provide inference for independent or paired samples. The multiplier central limit theorem is used for calculating p-values of the Cramer-von Mises test statistic. Finite sample properties are assessed with Monte Carlo experiments. We apply the testing procedure on empirical examples infinance, psychology, insurance and medicine.

A New Modified Goodness of Fit Tests for Type 2 Censored Sample from Normal Population

In this paper a procedure is considered for a new modified goodness of fit test for the normal type2 censored population. Samples of sizes 10(10)60 are chosen and censored at a specified percentage. Cramer von Mises and Anderson Darling test statistics are used with a nonparametric density estimator in place of the empirical distribution function. Tables of critical values for the two tests are generated. The power of the tests for nine alternative distributions is shown. Results show high power of discriminating the alternatives.

Average projection type weighted Cramér- von Mises statistics for testing some distributions

This paper addresses the problem of testing goodness-of-fit for several important multivariate distributions: (I) Uniform distribution on p-dimensional unit sphere; (II) multivariate standard normal distribution; and (III) multivariate normal distribution with unknown mean vector and covariance matrix. The average projection type weighted Cramer-von Mises test statistic as well as estimated and weighted Cramer-von Mises statistics for testing distributions (I), (II) and (III) are constructed via integrating projection direction on the unit sphere, and the asymptotic distributions and the expansions of those test statistics under the null hypothesis are also obtained. Furthermore, the approach of this paper can be applied to testing goodness-of-fit for elliptically contoured distributions.

An L1-variant of the Cramer-von Mises test

An L 1-variant of the Cramer-von Mises test statistic for the one sample test of fit problem is presented. Quantiles of the sampling distribution under the null hypothesis are derived by Monte-Carlo Simulation. The power of the new test is compared to those of other, conventional one sample tests, such as the Cramer-von Mises test, the Anderson-Darling test, and the Kolmogorov test.

On cramér-von mises tests of goodness of fit with censored data

The paper considers the goodness of fit tests with right censored data or doubly censored data. The Fredholm Integral Equation (FIE) method proposed by Ren (1993) is implemented in the simulation studies to estimate the null distribution of the Cramer-von Mises test statistics and the asymptotic covariance function of the self-consistent estimator for the lifetime distribution with right censored data or doubly censored data. We show that for fixed alternatives, the bootstrap method does not estimate the null distribution consistently for doubly censored data. For the right censored case, a comparison between the performance of FIE and the η out of η bootstrap shows that FIE gives better estimation for the null distribution. The application of FIE to a set of right censored Channing House data and to a set of doubly censored breast cancer data is presented.

A review of model selection procedures relevant to the weibull distribution

A number of goodness-of-fit and model selection procedures related to the Weibull distribution are reviewed. These procedures include probability plotting, correlation type goodness-of-fit tests, and chi-square goodness-of-fit tests. Also the Kolmogorow-Smirniv, Kuiper, and Cramer-Von Mises test statistics for completely specified hypothesis based on censored data are reviewed, and these test statistics based on complete samples for the unspecified parameters case are considered. Goodness-of-fit tests based on sample spacings, and a goodness-of-fit test for the Weibull process, is also discussed. Model selection procedures for selecting between a Weibull and gamma model, a Weibull and lognormal model, and for selecting from among all three models are considered. Also tests of exponential versus Weibull and Weibull versus generalized gamma are mentioned.