Behaviour of the length test for medium sample sizes

In this note it is shown that even for relatively large sample sites the asymptotic distribution of the smoothed length as derived in Reschenhofer and Bomse (1991) should not be used for the determination of critical values. Therefore extended tables of critical values for both the 1% and 5% levels of significance generated by simulation are presented.     

On goodness of fit tests based on spacings for type ii censored samples

A class of tests based on spacings is obtained for milticensored samples. Their asymptotic null as well as alternative distributions are obtained.     

Assessing the fit of finite mixture distributions

Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literature can be found on tests for assessing their goodness of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicit use of the mixture structure. In a simulation study the tests are compared to some traditional goodness of fit tests that, however, are not customised for mixture distributions. The first smooth test has overall good power and generally outperforms the other tests. The second smooth test is particularly suitable for assessing the fit of each component distribution separately. The tests are applicable to both continuous and discrete distributions and they are illustrated on three medical data sets.     

Moments of nonparametric probability density functions of entropy estimators applied to testing the inverse Gaussian distribution

The inverse Gaussian (IG) distribution is widely used to model data and then it is important to develop efficient goodness of fit tests for this distribution. In this article, we introduce some new test statistics for examining the IG goodness of fit based on correcting moments of nonparametric probability density functions of entropy estimators. These tests are consistent against all alternatives. Critical points and power of the tests are explored by simulation. We show that the proposed tests are more powerful than competitor tests. Finally, the proposed tests are illustrated by real data examples.     

Empirical behavior of some tests for normality

The behavior of a range of tests assessing the normality of a sequence of independent and identically distributed random variables is investigated.An examination of the empirical significance level of the tests is undertaken for different sample sizes. The empirical power associated with these tests is also calculated under some alternative distributions.     

A simple test for equally likely random responses in a sequence of bernoulli trials

A simple versatile combinatorial test is given for the null hypothesis that the two kinds of responses in a sequence of binary random variables are both equiprobable and randomly distributed. It is sensitive to a preponderance of either kind of response in either of two pre-selected halves of the positions of the sequence, e.g., the right half vs. the left, or the center vs. both ends. It combines the nice features of being, on the one hand, relatively assumption free and easy to apply and, on the other hand, sensitive to basic patterns underlying a poor fit of the empirical distribution to a theoretical model.     

Comparison of goodness of fit tests for the cox proportional hazards model

The proportional hazards regression model of Cox(1972) is widely used in analyzing survival data. We examine several goodness of fit tests for checking the proportionality of hazards in the Cox model with two-sample censored data, and compare the performance of these tests by a simulation study. The strengths and weaknesses of the tests are pointed out. The effects of the extent of random censoring on the size and power are also examined. Results of a simulation study demonstrate that Gill and Schumacher's test is most powerful against a broad range of monotone departures from the proportional hazards assumption, but it may not perform as well fail for alternatives of nonmonotone hazard ratio. For the latter kind of alternatives, Andersen's test may detect patterns of irregular changes in hazards.     

On a test for exponentiality against Laplace order dominance

Surles and Padgett recently introduced two-parameter Burr Type X distribution, which can also be described as the generalized Rayleigh distribution. It is observed that the generalized Rayleigh and log-normal distributions have many common properties and both the distributions can be used quite effectively to analyze skewed data set. For a given data set the problem of selecting either generalized Rayleigh or log-normal distribution is discussed in this paper. The ratio of maximized likelihood (RML) is used in discriminating between the two distributing functions. Asymptotic distributions of the RML under null hypotheses are obtained and they are used to determine the minimum sample size required in discriminating between these two families of distributions for a used specified probability of correct selection and the tolerance limit.     

Smooth goodness of fit tests for the weibull distribution with singly censored data

The smooth goodness of fit tests are generalized to singly censored data and applied to the problem of testing Weibull (or extreme value) fit. Smooth tests, Pearson-type tests, and the spacings tests proposed by Mann, Schemer, and Fertig (1973) are compared on the basis of local asymptotic relative efficiency with respect to the asymptotic best test against generalized gamma alternatives, The smooth test of order one Is found to be most efficient for the generalized gamma alternatives.     

A modified Kolmogorov-Smirnov test for the inverse gaussian density with unknown parameters

The Kolmogorov-Smirnov (KS) test is an empirical distribution function (EDF) based goodness-of-fit test that requires the underlying hypothesized density to be continuous and completely specified. When the parameters are unknown and must be estimated from the data, standard tables of the KS test statistic are not valid. Approximate upper tail percentage points of the KS statistic for the inverse Gaussian (IG) distribution with unknown parameters are tabled in this paper.

A study of the power of the KS test for the IG distribution indicates that the test is able todiscriminate between the IG distribution and distributions such as the uniform and exponentialdistributions that are very different in shape, but is relatively unable to discriminate between the IG distribution and distributions that are similar in shape such as the lognormal and Weibull distributions. In modeling settings the former distinction is typically more important to make than the latter distinction.     

A powerful test for multivariate normality

This paper investigates a new test for normality that is easy for biomedical researchers to understand and easy to implement in all dimensions. In terms of power comparison against a broad range of alternatives, the new test outperforms the best known competitors in the literature as demonstrated by simulation results. In addition, the proposed test is illustrated using data from real biomedical studies.     

One sample tests of location for nonnormal symmetric data

A score test of location is derived for data from a distorted normal distribution. A simulation study compares the performance of this test to the t-test and Wilcoxon test for symmetric data from such a distribution. For this type of data the score test can be considerably more powerful than both the t-test and Wilcoxon test. This suggests that such a score test may be useful in practice when variations from normality can be modeled by such a family of distributions.     

Smooth tests of fit for censored gmma samples

In this paper properties of two estimators of Cpm are investigated in terms of changes in the process mean and variance. The bias and mean squared error of these estimators are derived. It can be shown that the estimate of Cpm proposed by Chan, Cheng and Spiring (1988) has smaller bias than the one proposed by Boyles (1991) and also has a smaller mean squared error under certain conditions. Various approximate confidence intervals for Cpm are obtained and are compared in terms of coverage probabilities, missed rate and average interval width.     

On the sample size of curtailed tests

Formulas are given for the asymptotic distribution, mean, and variance of m^-1N_m,where NN_m is the random sample size of the curtailed version of a fixed-sample most powerful test based on sample size m. The adequacy of the formulas is numerically investigated in some important applications where exact formulas can also be derived     

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.     

Chi-square tests for multivariate normality with application to common stock prices

The theory of chi-square tests with data-dependent cells is applied to provide tests of fit to the family of p-variate normal distributions. The cells are bounded by hyperellipses (x-[Xbar])'S^-1 (x-[Xbar]) = c_i centered at the sample mean [Xbar] and having shape deter-mined by the sample covariance matrix S. The Pearson statistic with these cells is affine-invariant, has a null distribution not depending on the true mean and covariance, and has asymptotic critical points between those of x² (M-1) and x² (M-2) when M cells are employed. The test is insensitive to lack of symmetry, but peakedness, broad shoulders and heavy tails are easily discerned in the cell counts. Multivariate normality of logarithms of relative prices of common stocks, a common assumption in finan-cial markets theory, is studied using the statistic described here and a large data base.     

Small sample distribution for a nonparametric test for trend

The exact distribution of a nonparametric test statistic for ordered alternatives, the _rank ² statistic, is computed for small sample sizes. The exact distribution is compared to an approximation.     

Goodness of fit tests for Nakagami distribution based on smooth tests

ABSTRACT

Nakagami distribution is one of the most common distributions used to model positive valued and right skewed data. In this study, we interest goodness of fit problem for Nakagami distribution. Thus, we propose smooth tests for Nakagami distribution based on orthonormal functions. We also compare these tests with some classical goodness of fit tests such as Cramer–von Mises, Anderson–Darling, and Kolmogorov–Smirnov tests in respect to type-I error rates and powers of tests. Simulation study indicates that smooth tests give better results than these classical tests give in respect to almost all cases considered.     

Exact and approximate distributions of the chi-square statistic for equiprobability

The distribution of the chi-square goodness-of-fit statistic is studied in the equiprobable case. Tables of exact critical values are given for a = .1, .05, .01, .005; k = 2(1)4, N = 26(1)50; k = 5, N = 26(1)40; k = 6(1)10, N = 26(1)30, where a is the desired significance level, k is the number of cells and N is the sample size. Methods of fitting the true distribution are compared. If k> 3, it is found that a simple additive adjustment to the asymptotic chi-square fit leads to high accuracy even for N between 10 and 20. For k = 2, the Yates corrected chi-square statistic is very accurately fitted by the usual chi-square distribution.