A note on circular neighbor balanced designs

ABSTRACT

This paper describes some methods of constructing circular neighbor balanced and circular partially neighbor balanced block designs for estimation of direct and neighbor effects of the treatments. A class of circular neighbor balanced block designs with unequal block sizes is also proposed.     

A Likelihood Integrated Method for Exploratory Graphical Analysis of Change Point Problem with Directional Data

In this article we introduce a new likelihood based method, called the likelihood integrated method, which is distinct from the well-known integrated likelihood method. We use the likelihood integrated to propose a simple exploratory graphical analysis for the change point problem in the context of directional data. The method is applied to analysis of two real life data sets. The results obtained by application of this simple method are seen to be quite similar to those obtained earlier by different formal methods in most cases. A small simulation study is conducted to assess the effectiveness of this procedure in indicating presence of change point.     

Estimation of Population Mean Using Known Coefficient of Variation of the Study Character in the Presence of Non Response

Using the known coefficient of variation of the study character, generalized and regression-type estimators for the population mean using two phase sampling in the presence of non response were proposed and their properties have been studied. The conditions under which the proposed estimators are more efficient than the relevant estimators have been obtained. The empirical studies were given in the support of the problems in the case of positive and negative correlation between the study and the auxiliary characters which show the increase in the efficiency of the proposed estimators using known coefficient of variation of the study character with respect to the relevant estimators.     

A Note on Testing Homogeneity of Several Exponential Location Parameters

In this article, the problems of testing homogeneity of several exponential location parameters against simple and tree ordered alternatives are considered separately. Test procedures for both the alternatives are proposed using restricted maximum likelihood estimators (RMLE) of exponential location parameters under the respective orderings. Critical constants for the implementation of the proposed procedures are tabulated. Power comparison of the proposed test procedure under the simple ordered alternative with the procedure of Chen (1982 Chen , H. J. ( 1982 ). A new range statistic for comparisons of several exponential location parameters . Biometrika 69 ( 1 ): 257 – 260 .[Crossref], [Web of Science ®] , [Google Scholar]) and of Dhawan and Gill (1999 Dhawan , A. K. , Gill , A. N. ( 1999 ). A one-sided test for testing homogeneity of scale parameters against ordered alternative . Communication in Statistics—Theory and Methods 28 ( 10 ): 2417 – 2439 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is carried out using Monte-Carlo simulation.     

On an Extended Version of Skew Generalized Normal Distribution and Some of its Properties

Abstract

A generalization of Chauvenet's test (see Bol'shev, L. N. 1969 Bol'shev, L. N. 1969. On tests for rejecting outlying observations. Trudy In-ta prikladnoi Mat. Tblissi Gosudart. univ., 2: 159–177. (In Russian) [Google Scholar]. On tests for rejecting outlying observations. Trudy In-ta prikladnoi Mat. Tblissi Gosudart. univ. 2:159–177. (In Russian); Voinov, V. G., Nikulin, M. N. 1996 Voinov, V. G. and Nikulin, M. N. 1996. Unbaised Estimators and Their Applications Vol. 2, Kluwer Academic Publishers.  [Google Scholar]. Unbaised Estimators and Their Applications. Vol. 2. Kluwer Academic Publishers.) suitable to applied the problem of detecting r outliers in an univariate data set is proposed. In the exponential case, the Chauvenet's test can be used. Various modifications of this test were considered by Bol'shev, Ibrakimov and Khalfina (Ibrakimov, I. A., Khalfina 1978 Ibrakimov, I. A. and Khalfina. 1978. Some asymptotic results concerning the Chauvenet test. Ter. Veroyatnost. i Primenen., 23(3): 593–597.  [Google Scholar]. Some asymptotic results concerning the Chauvenet test. Ter. Veroyatnost. i Primenen. 23(3):593–597.), Greenwood and Nikulin (Greenwood, Nikulin, P. E. 1996 Greenwood and Nikulin, P. E. 1996. A Guide to Chi-Squared Testing New York: John Wiley and Sons, Inc..  [Google Scholar]. A Guide to Chi-Squared Testing. New York: John Wiley and Sons, Inc.) depending on the choice of the estimation method used: MLE or MVUE. As procedures for testing one outlier in exponential model have been investigated by a number of authors including Chikkagoudar and Kunchur (Chikkagoudar, M. S., Kunchur, S. H. 1983 Chikkagoudar, M. S. and Kunchur, S. H. 1983. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth., 12: 2127–2142. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127–2142.), Lewis and Fieller (Lewis, T., Fiellerm N. R. J. 1979 Lewis, T. and Fiellerm, N. R. J. 1979. A recursive algorithm for null distribution for outliers: I. Gamma samples. Technometrics, 21: 371–376. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. A recursive algorithm for null distribution for outliers : I. Gamma samples. Technometrics 21:371–376.), Likes (Likes, J. 1966 Likes, J. 1966. Distribution of Dixon's statistics in the case of an exponential population. Metrika, 11: 46–54. (91, 96, 136, 198–200, 204, 209, 210)[Crossref] , [Google Scholar]. Distribution of Dixon's statistics in the case of an exponential population. Metrika 11:46–54. (91, 96, 136, 198–200, 204, 209, 210).) and Kabe (Kabe, D. G. 1970 Kabe, D. G. 1970. Testing outliers from an exponential population. Metrika, 15: 15–18. [Crossref], [Web of Science ®] , [Google Scholar]. Testing outliers from an exponential population. Metrika 15:15–18.); only two types of statistics for testing multiple outliers exist. First is Dixon's while the second is based on the ratio of the sum of the observations suspected to be outliers to the sum of all observations of the sample. In fact, most of these authors have considered a general case of gamma model and the results for exponential model are given a special case. The object of the present communication is to focus on alternative models, namely slippage alternatives (see Barnett, Vic., Toby Lewis 1978 Barnett, Vic. and Toby, Lewis. 1978. Outlier in Statistical Data New York: John Wiley and Sons, Inc..  [Google Scholar]. Outlier in Statistical Data. New York: John Wiley and Sons, Inc.) in exponential samples. We propose a statistic different from the well known Dixon's statistic D_r to test for multiple outliers. Distribution of the test based on this new statistic under slippage alternatives is obtained and hence the tables of critical values are given, for various n (size of the sample) and r (the number of outliers). The power of the new test is also calculated, it is compared to the power of the Dixon's statistic (Chikkagoudar, M. S., Kunchur, S. H. 1983 Chikkagoudar, M. S. and Kunchur, S. H. 1983. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth., 12: 2127–2142. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. Distribution of test statistics for multiple outliers in exponential samples. Comm. Stat. Theory. and Meth. 12:2127–2142.). Notice that the new statistic based test power is greater the Dixon's statistic based test one.     

Estimation using hybrid censored data from a generalized inverted exponential distribution

ABSTRACT

We consider point and interval estimation of the unknown parameters of a generalized inverted exponential distribution in the presence of hybrid censoring. The maximum likelihood estimates are obtained using EM algorithm. We then compute Fisher information matrix using the missing value principle. Bayes estimates are derived under squared error and general entropy loss functions. Furthermore, approximate Bayes estimates are obtained using Tierney and Kadane method as well as using importance sampling approach. Asymptotic and highest posterior density intervals are also constructed. Proposed estimates are compared numerically using Monte Carlo simulations and a real data set is analyzed for illustrative purposes.     

On generalized hyper-Poisson distribution of order k and its application

ABSTRACT

Here we introduce a new class of distributions namely the generalized hyper-Poisson distribution of order k (GHPD(k)) as an order k version of the alpha-generalized hyper-Poisson distribution of Kumar and Nair (Statistica, 2014b Kumar, C.S., Nair, B.U. (2014b). A three parameter hyper-Poisson distribution and some of its properties. Statistica. 74(2):183–198. [Google Scholar]). Several properties of the GHPD(k) are derived and the estimation of the parameters of the distribution by the method of mixed moments and the method of maximum likelihood is discussed. Certain testing procedures are suggested and all these estimation and testing procedures are illustrated with the help of a real-life data set. Further a simulation study is conducted.     

Negative moments of a modified power series distribution and bias of the maximum likelihood estimator

The class of Modified Power Series distributions (MPSD) containing Lagrangian Poisson (LPD) (Consul and Jain, 1973) and Lagrangian binomial distributions (LBD) (Jain and Consul, 1971) was studied by Gupta (1974). We investigate the problem of finding the negative momentsE[X^-r ], of displaced and decapitated Modified Power Series Distributions. We derive the relationship between rand (r-1) negative moments. The negative moments of the decapitated and displaced LPD are obtained. These results are, then, used to find the exact amount of bias in the ML estimators of the parameters in the LPD and the LBD. We have also given the variances of the ML estimator and the minimum variance unbiased estimator of the parameter in the LPD.