New Goodness Of Fit Test Research Articles

Gini index based goodness-of-fit test for the Lindley distribution

In survival analysis and reliability studies the Lindley distribution has been widely used. In this article, we introduce a new goodness of fit test for the Lindley distribution based on an estimate of the Gini index. The asymptotic distribution of the new test statistic is investigated. The unknown parameter of the Lindley distribution is estimated by the maximum likelihood estimator. The critical points and the actual sizes of the test are obtained by Monte Carlo simulations. A power comparison study of the existing tests is performed. It is shown that the Gini index-based test that we proposed performs well by comparing its powers with that of other tests. A real-life data analysis is finally presented for illustrative purpose.

A new goodness of fit test for gamma distribution with censored observations

In the present paper, we develop a new goodness of fit test for gamma distribution based on the fixed point characterization. We use U-Statistics theory to derive the test statistic. We discuss how the right censored observations are incorporated into the proposed test. The asymptotic properties of the test statistics in censored and uncensored cases are studied. We carry out a Monte Carlo simulation study to validate the finite sample performance of the proposed tests. We also illustrate the test procedures using real data sets.

Goodness of fit test for uniform distribution with censored observation.

We develop new goodness of fit test for uniform distribution based on a conditional moment characterization. We study the asymptotic properties of the proposed test statistic. We also present a goodness of fit test for uniform distribution to incorporate the right censored observations and studied its properties. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the proposed tests. We illustrate the test procedures using real data sets.

Some New Goodness of Fit Tests Based on Sample Spacings

Some New Goodness of Fit Tests Based on Sample Spacings

A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

A new goodness of fit test for multivariate normality

This paper presents a multivariate Kolmogorov-Smirnov (MVKS) goodness of fit test for multivariate normality. The proposed test is based on the difference between the empirical distribution function and the theoretical distribution function. While calculating them in multivariate case, the problem is that the variables cannot be distribution-free as in the univariate case. Firstly, the variables are made independent to solve this problem and the Rosenblatt transform is applied for independence of variates. Then the theoretical and empirical distribution values are calculated and the MVKS test statistic is computed. It provides an easy calculation for d-dimensional data by using the same algorithm and critical table values. This paper demonstrates the effectiveness of the MVKS for different dimensions with a simulation study which also includes the comparison of the MVKS critical tables with univariate Kolmogorov-Smirnov (KS) critical table and the power comparisons of the MVKS (bivariate case) against with the existing bivariate normality tests. Lastly, the MVKS is applied to two different multivariate data sets to confirm that it achieves consistent, accurate and correct results.

A unified model-implied instrumental variable approach for structural equation modeling with mixed variables

The model-implied instrumental variable (MIIV) estimator is an equation-by-equation estimator of structural equation models that is more robust to structural misspecifications than full information estimators. Previous studies have concentrated on endogenous variables that are all continuous (MIIV-2SLS) or all ordinal . We develop a unified MIIV approach that applies to a mixture of binary, ordinal, censored, or continuous endogenous observed variables. We include estimates of factor loadings, regression coefficients, variances, and covariances along with their asymptotic standard errors. In addition, we create new goodness of fit tests of the model and overidentification tests of single equations. Our simulation study shows that the proposed MIIV approach is more robust to structural misspecifications than diagonally weighted least squares (DWLS) and that both the goodness of fit model tests and the overidentification equations tests can detect structural misspecifications. We also find that the bias in asymptotic standard errors for the MIIV estimators of factor loadings and regression coefficients are often lower than the DWLS ones, though the differences are small in large samples. Our analysis shows that scaling indicators with low reliability can adversely affect the MIIV estimators. Also, using a small subset of MIIVs reduces small sample bias of coefficient estimates, but can lower the power of overidentification tests of equations.

An estimation of Phi divergence and its application in testing normality

In this article, a new goodness of fit test for normality is introduced based on Phi divergence. The test statistic is estimated using spacing and the consistency of the test is proved. Then with replacing some special cases of Phi divergence, the efficiency of each test statistic is analyzed by Monte Carlo simulation against some competitors (based on Phi divergence using kernel density function and also some classical competitors). It is shown that each special case of Phi divergence based test is the most powerful in each group of alternatives (depending on symmetry or support).

Point estimation and two new goodness of fit tests for the scale family based on general progressively Type-II censored samples

In this paper, we obtain an analytic and explicit estimator of the scale parameter using pivotal method and propose two new goodness of fit tests for the scale family based on general progressively Type-II censored samples. The properties about the test statistics are studied. Furthermore, we apply our methods to some specific life distributions for illustration. Moreover, we obtain critical values by simulations and compare the power of the two tests against various alternatives under many censoring schemes. We also obtain the empirical significance levels thorough Monte Carlo simulation. We do the comparison of the proposed estimator with the existing estimators given in the literature by means of a power study. The influence of the parameter in the alternative distribution to power is explored. The simulation results are presented using data visualization. We conclude that the estimator we derive and tests we propose perform well in many cases. Finally, a numerical example is presented.

A goodness of fit test for multilevel survival data

ABSTRACTNo satisfactory goodness of fit test is available for multilevel survival data which occur when survival data are clustered or hierarchical in nature. Hence the aim of this research is to develop a new goodness of fit test for multilevel survival data and to examine the properties of the newly developed test. Simulation studies were carried out to evaluate the type І error and the power. The results showed that the type I error holds for every combination tested and that the test is powerful against the alternative hypothesis of nonproportional hazards for all combinations tested.

Warp statistics and financial returns

ABSTRACTWe introduce a new approach to financial returns and data analysis based on an infinite family of statistics called warp statistics. These statistics provide evidence that certain distributions such as the stable distributions are not good models for the financial returns from various securities or indexes like the S&P 500 and the Dow Jones. As statistics for general random variables, these numbers often appear to converge in simulations and we give several examples where the reciprocal of the first warp statistic appear to converge to the Hausdorff dimension. For any normal random variable, simulations suggest that the first and second warp statistics are and which provides new goodness of fit tests for normality. We give explicit formulas for the first and second warp statistics that are easily evaluated by a computer which makes this theory particularly suitable for applications.

New goodness of fit tests for the Cauchy distribution

ABSTRACTSome goodness-of-fit procedures for the Cauchy distribution are presented. The power comparisons indicate that the new tests possess good performances among the competitors, especially against symmetric alternatives. A financial data set is analyzed for illustration.

A Goodness of Fit Test for the Multilevel Logistic Model

It is crucial to test the goodness of fit of a model before it is used to make statistical inferences. However, no satisfactory goodness of fit test is available for the case of categorical multilevel data which occur when categorical data are clustered or hierarchical in nature. Hence the aim of this paper is to develop a new goodness of fit test for multilevel binary data based on Hosmer and Lemeshow and Lipsitz et.al. In order to identify the properties of the developed test, simulation studies were carried out to assess the Type I error and the power.

On asymptotic efficiency of goodness of fit tests for Pareto distribution based on characterizations

In this paper we present a characterization for Pareto distribution. We propose two new goodness of fit tests based on this characterization and two tests based on Rossberg?s characterization. We calculate their Bahadur efficiencies against different alternatives and compare the tests. We also find a class of locally optimal alternatives for each test.

New Goodness of Fit Tests Based on Stochastic EDF

A new approach of randomization is proposed to construct goodness of fit tests generally. Some new test statistics are derived, which are based on the stochastic empirical distribution function (EDF). Note that the stochastic EDF for a set of given sample observations is a randomized distribution function. By substituting the stochastic EDF for the classical EDF in the Kolmogorov–Smirnov, Cramér–von Mises, Anderson–Darling, Berk–Jones, and Einmahl–Mckeague statistics, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. In comparison to existing tests, it is shown, by a simulation study, that the new test statistics are generally more powerful than the corresponding ones based on the classical EDF or modified EDF in most cases.

A New Goodness of Fit Test for the Logistic Distribution

Abstract The logistic distribution is often used in survival analysis and biological studies to model growth curves. In this paper we present a method to test if the available data come from a logistic distribution. The proposed test is a modification of the Greenwood statistic based on higher order spacings as proposed by Rao and Kuo (1984). Parameters of the distribution are estimated by the method of moments and the method of maximum likelihood in order to compute the test statistic. Power comparisons of the test for both methods of estimation are carried out via simulations. It is concluded that the test statistic based on the method of moments has higher power.

Classifying Speech Sonority Functional Data using a Projected Kolmogorov–Smirnov Approach

This paper addresses a linguistically motivated question of classification of functional data, namely the statistical classification of languages according to their rhythmic features. This is an important open problem in phonology. The analysis is based on the information provided by the sonority, which is an index of local regularity of the speech signal. Our main tool is the projected Kolmogorov–Smirnov test. This is a new goodness of fit test for functional data. The result obtained supports the linguistic conjecture of the existence of three rhythmic classes.

Testing exponentiality by comparing the empirical distribution function of the normalized spacings with that of the original data

We introduce new goodness of fit tests for exponentiality by using a characterization based on normalized spacings. We provide relevant asymptotic theory for these tests and study their efficiency. An empirical power study and comparisons are also provided.

A new goodness of fit test for the equality of multinomial cell probabilities versus trend alternatives

In this paper, a new test statistic is presented for testing the null hypothesis of equal multinomial cell probabilities versus various trend alternatives. Exact asymptotic critical values are obtained, The power of the test is compared with several other statistics considered by Choulakian et al (1995), The test is shown to have better power for certain trend alternatives.