Rank Tests for Independence Against Weighted Alternative with Missing Values

One of the common problems of practical importance is that of determining whether there is independence between a pair of random variables. In this paper, the problem of testing independence of bivariate random variables against a weighted alternative model with possible missing values on both responses is considered. The model considered here is due to Shei, Bai and Tsai [9] which is the generalization of Hajek and Sidak [12] model with weighted contamination. A new rank test based on ranks is proposed and its asymptotic normality is established. Locally most powerful tests for the model is derived. The asymptotic null distributions of the test statistics are also provided for the purpose of practical us

PROCEDURE FOR DETECTING ‘MORE NBU-NESS’ PROPERTY OF LIFE DISTRIBUTIONS

Testing the hypothesis of no ageing against positive ageing has been considered by many authors in the literature. However, very fewtests procedures for detecting whether a life distribution possesses ‘more positive ageng’ than the other distribution are developed.Hollander, Park and Proschan(1986) proposed a test procedure to detect ‘More NBUness’ property of life distributions. Pandit and Gudaganavar(2009) developeda procedure which is an improvementover the test due to Hollander, Park and Proschan(1986). In this paper, a test is developed to decide whether onelife distribution possesses more ‘new better than used’ (NBU)property than does another life distribution. The asymptotic performance of the test procedure is evaluated interms of Pitman asymptotic relative efficiency. It is found that new test performs betterthan the tests in the literature

A Nonparametric Control Chart for Location Based on Sub-Samples of Size Two

Control charts are widely used in statistical process control to detect changes in a production process and for monitoring a process to make sure that it is in control. In conventional statistical process control, the pattern of chance causes is often assumed to follow normal distribution. It is well known that the assumption of normality or any specific parametric form for the process distribution is too restrictive. In such situations, distribution-free or nonparametric control charts can serve the purpose better. In this paper, distribution-free control charts are developed based on a class of one-sample test statistics with sub-samples of size two due to Mehra, Prasad and Madhava Rao (Austral. J. Statist. 32: 373392, 1990). The control charts based on their statistic (-chart) are easy to understand and to use. The performance of the proposed procedures is studied through the average run length, which is the expected number of samples required by the procedure to signal out of control. It is observed that the performance of the proposed chart is better than the existing charts in the literature

On Two-sample Test for Detecting Differences in the IFR Property of Life Distributions

A test proposed for testing whether one distribution is more Increasing Failure Rate (IFR) than another, based on a measure of IFR is presented in this paper. The asymptotic normality of the proposed test statistic was also established. The asymptotic null variance from the data was estimated since the variance depends on the unknown distribution. The Pitman asymptotic efficacies of the proposed test statistic are computed for various alternative IFR distributions

A Note on Detecting “More IFR-ness” Property of Life Distributions

In this paper, a problem of testing whether one life distribution possesses “more IFR” property than the other is considered.A new test procedure is proposed and the distribution of the test statistic is studied. The performance of the procedure is evaluated in terms of Pitman asymptotic relative efficiency. The consistency property of the test procedure is established. It is observed that the new procedure is better than the existing procedure in the literatur

TEST PROCEDURES FOR DETECTING ‘MORE NBUNESS’ PROPERTY OF LIFE DISTRIBUTIONS

Testing the hypothesis of no ageing against positive ageing has been considered by many authors in the literature. However, very few tests procedures for detecting whether a life distribution possesses ‘more positive ageng’ than the other distribution are developed. Hollander, Park and Proschan (1986) proposed a test procedure to detect ‘More NBU-ness’ property of life distributions, Pandit and Gudaganavar (2009) developed a procedure which is an improvement over the test due to Hollander, Park and Proschan (1986). In this paper, a test is developed to decide whether one life distribution possesses more ‘new better than used’ (NBU) property than does another life distribution. The asymptotic performance of the tes

A new class of distribution-free tests for special twosample location problem

A particular type of two-sample problem of comparing the performances of two packing machines in which one machine may underfill the packets and the other may overfill the packets on an average. Such problems can be studied under special two-sample location setup wherein one wishes to test for the point of symmetry versus an appropriate alternative. In this paper a class of test statistics based on sub-samples is proposed. From the Asymptotic Relative Efficiencies (ARE's), it is concluded that the members of proposed classes of tests perform better than the test due to Shetty and Umarani (2005), for those distributions considered for evaluation

Analysis of dental caries using generalized linear and count regression models

Generalized linear models (GLM) are generalization of linear regression models, which allow fi tting regression models to response data in all the sciences especially medical and dental sciences that follow a general exponential family. These are fl exible and widely used class of such models that can accommodate response variables. Count data are frequently characterized by overdispersion and excess zeros. Zero-infl ated count models provide a parsimonious yet powerful way to model this type of situation. Such models assume that the data are a mixture of two separate data generation processes: one generates only zeros, and the other is either a Poisson or a negative binomial data-generating process. Zero infl ated count regression models such as the zero-infl ated Poisson (ZIP), zeroinfl ated negative binomial (ZINB) regression models have been used to handle dental caries count data with many zeros. We present an evaluation framework to the suitability of applying the GLM, Poisson, NB, ZIP and ZINB to dental caries data set where the count data may exhibit evidence of many zeros and overdispersion. Estimation of the model parameters using the method of maximum likelihood is provided. Based on the Vuong test statistic and the goodness of fi t measure for dental caries data, the NB and ZINB regression models perform better than other count regression model

On Robustness of a Sequential Test for Scale Parameter of Gamma and Exponential Distributions

The main aim of the present paper is to study the robustness of the developed sequential probability ratio test (SPRT) for testing the hypothesis about scale parameter of gamma distribution with known shape parameter and exponential distribution with location parameter. The robustness of the SPRT for scale parameter of gamma distribution is studied when the shape parameter has undergone a change. The similar study is conducted for the scale parameter of exponential distribution when the location parameter has undergone a change. The expressions for operating characteristic and average sample number functions are derived. It is found in both the cases that the SPRT is robust only when there is a slight variation in the shape and location parameter in the respective distributions

Distribution-Free Tests for Two-Sample Location Problems Based on Subsamples

Nonparametric tests for location problems have received much attention in the literature. Many nonparametric tests have been proposed for one, two and several samples location problems. In this paper a class of test statistics is proposed for two sample location problem when the underlying distributions of the samples are symmetric. The class of test statistics proposed is linear combination of U-statistics whose kernel is based on subsamples extrema. The members of the new class are shown to be asymptotically normal. The performance of the proposed class of tests is evaluated using Pitman Asymptotic Relative Efficiency. It is observed that the members of the proposed class of tests are better than the existing tests in the literature