Statistics

Previous months: - 1003(10) - 1004(7) - 1005(4) - 1006(1) - 1007(2) - 1008(4) - 1010(1) - 1011(1) - 1105(2) - 1107(1) - 1111(1) - 1112(1)

Recent Submissions

Any replacements are listed further down

[35] viXra:1112.0092 [pdf] submitted on 2011-12-31 06:41:31

Gauss Distribution-a Complete Proof Only Ita

Authors: Leonardo Rubino
Comments: 13 Pages.

In this paper (for the moment in Italian language only-sorry) you can find a rare proof of the Gauss Distribution Law, as almost all available books (in the opinion of who is writing) just show it, without giving any demonstration. Then, here you can also find a description of the 3-sigma rule, very used in the field of technologies. At last, a peculiarity of the quantum mechanics is here highlighted, where the claim of the equality sign in the Heisenberg indetermination equations leads to a Gaussian wave function, indeed, which reduces to a minimum value the quantum uncertainty situation.
Category: Statistics

[34] viXra:1111.0073 [pdf] submitted on 21 Nov 2011

Kullback-Leibler Simplex

Authors: Popon Kangpenkae
Comments: 12 pages

This technical reference presents the functional structure and the algorithmic implementation of KL (Kullback-Leibler) simplex. It details the simplex approximation and fusion. The KL simplex is fundamental, robust, adaptive an informatics agent for computational research in economics, finance, game and mechanism. From this perspective the study provides comprehensive results to facilitate future work in such areas.
Category: Statistics

[33] viXra:1107.0049 [pdf] submitted on 24 Jul 2011

Studies in Sampling Techniques and Time Series Analysis

Authors: Rajesh Singh, Florentin Smarandache
Comments: 72 pages

This book has been designed for students and researchers who are working in the field of time series analysis and estimation in finite population. There are papers by Rajesh Singh, Florentin Smarandache, Shweta Maurya, Ashish K. Singh, Manoj Kr. Chaudhary, V. K. Singh, Mukesh Kumar and Sachin Malik. First chapter deals with the problem of time series and the rest of four chapters deal with the problems in estimation in finite population.
Category: Statistics

[32] viXra:1105.0038 [pdf] submitted on 25 May 2011

The Numerical Generalised Least-Squares Estimator of an Unknown Constant Mean of Randon Field

Authors: T Suslo
Comments: 9 pages.

We constraint on computer the best linear unbiased generalized statistics of random field for the best linear unbiased generalized statistics of an unknown constant mean of random field and derive the numerical generalized least-squares estimator of an unknown constant mean of random field. We derive the third constraint of spatial ststistics and show that the classic generalized least-squares estimator of an unknown constant mean of the field is only an asymptotic disjunction of the numerical one.
Category: Statistics

[31] viXra:1105.0026 [pdf] submitted on 16 May 2011

Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution

Authors: Elia Liitiäinen
Comments: 37 pages, Submitted to a journal

We study the moments E[d1,kα] of the k-th nearest neighbor distance for independent identically distributed points in Rn. In the earlier literature, the case α > n has been analyzed by assuming a bounded support for the underlying density. The boundedness assumption is removed by assuming the multivariate Gaussian distribution. In this case, the nearest neighbor distances show very different behavior in comparison to earlier results. In the unbounded case, it is shown that E[d1,kα] is asymptotically proportional to M-1 logn-1-α/2M instead of M-α/n as in the previous literature.
Category: Statistics

[30] viXra:1011.0070 [pdf] submitted on 29 Nov 2010

Determinants of Population Growth in Rajasthan: an Analysis

Authors: V.V. Singh, Alka Mittal, Neetish Sharma, Florentin Smarandache
Comments: 12 pages

Rajasthan is the biggest State of India and is currently in the second phase of demographic transition and is moving towards the third phase of demographic transition with very slow pace. However, state's population will continue to grow for a time period. Rajasthan's performance in the social and economic sector has been poor in past. The poor performance is the outcome of poverty, illiteracy and poor development, which co-exist and reinforce each other. There are many demographic and socio-economic factors responsible for population growth. This paper attempts to identify the demographic and socio-economic variables, which are responsible for population growth in Rajasthan with the help of multivariate analysis.
Category: Statistics

[29] viXra:1010.0054 [pdf] submitted on 20 Mar 2010

A Class of Separate-Type Estimators for Population Mean in Stratified Sampling Using Known Parameters Under Non-Response

Authors: Manoj K. Chaudhary, Rajesh Singh, Mukesh Kumar, Rakesh K. Shukla, Florentin Smarandache
Comments: 11 pages

The objective of the present paper is to propose a family of separate-type estimators of population mean in stratified random sampling in presence of nonresponse based on the family of estimators proposed by Khoshnevisan et al. (2007). Under simple random sampling without replacement (SRSWOR) the expressions of bias and mean square error (MSE) up to the first order of approximation are derived. The comparative study of the family with respect to usual estimator has been discussed. The expressions for optimum sample sizes of the strata in respect to cost of the survey have also been derived. An empirical study is carried out to shoe the properties of the estimators.
Category: Statistics

[28] viXra:1008.0044 [pdf] submitted on 16 Aug 2010

Degrees of Freedom: a Correction to Chi Square for Physical Hypotheses

Authors: John Michael Williams
Comments: 47 Pages.

In common practice, degrees of freedom (df) may be corrected for the number of theoretical free parameters as though parameters were the same as data categories. However, a free physical parameter generally is not equivalent to a data category in terms of goodness of the fit. Here we use synthetic, nonrandom data to show the effect of choice of categorization and df on goodness of fit. We then explain the origin of the df problem and show how to avoid it in a three-step process: First, the theoretical curve is fit to the data to remove its variance, leaving what, under the null hypothesis, should be structureless residuals. Second, the residuals are fit by a set of orthogonal polynomials up to the degree, should it occur, at which significant variance was removed. Third, the number of nonsignificant polynomial terms in the original + orthogonal set become the df in a standard chi square test. This process reduces a general df problem to one of polynomial df and allows goodness of a fit to be determined by data categorization and significance level alone. An example is given of an evaluation of physical data on neutrino oscillation.
Category: Statistics

[27] viXra:1008.0034 [pdf] submitted on 11 Aug 2010

Rural Migration a Significant Cause of Urbanization: a District Level Review of Census Data for Rajasthan

Authors: Jayant Singh, Hansraj Yadav, Florentin Smarandache
Comments: 8 pages

Migration plays an important role in urbanization of a state. In general more the migration higher the urbanization rate though it many not necessarily true in all the situations but in general it is witnessed that migration have a fairly large share in urbanization. A district level analysis for Rajasthan state is attempted to comprehend Urbanization due to migration their interlinkages and association.
Category: Statistics

[26] viXra:1008.0033 [pdf] submitted on 11 Aug 2010

Urbanization Due to Migration: a District Level Analysis of Migrants from Different Distances for the Rajasthan State

Authors: Jayant Singh, Hansraj Yadav, Florentin Smarandache
Comments: 10 pages

People migrate to different distances and there migration is governed by different reasons. Distance of place of migration plays an important role in the migration process and an analysis based on the remoteness of the origin and destination will reveal the push and pull factors in more explicit way. However, a common phenomenon is that people do migrate to a longer distance with a more focused objective and there propensity to settle in urban areas is always higher than the small distance migration.
Category: Statistics

[25] viXra:1008.0020 [pdf] submitted on 7 Aug 2010

A Family of Estimators for Estimating Population Mean in Stratified Sampling Under Non-Response

Authors: Manoj K. Chaudhary, Rajesh Singh, Rakesh K. Shukla, Mukesh Kumar, Florentin Smarandache
Comments: 8 pages

Khoshnevisan et al. (2007) proposed a general family of estimators for population mean using known value of some population parameters in simple random sampling. The objective of this paper is to propose a family of combined-type estimators in stratified random sampling adapting the family of estimators proposed by Khoshnevisan et al. (2007) under non-response. The properties of proposed family have been discussed. We have also obtained the expressions for optimum sample sizes of the strata in respect to cost of the survey. Results are also supported by numerical analysis.
Category: Statistics

[24] viXra:1007.0034 [pdf] submitted on 23 Jul 2010

On the Gini Mean Difference Arc-Lengths Test for Circular Data

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 15 pages.

In this paper, we propose a new test of uniformity on the circle based on the Gini mean difference of the sample arc-lengths, i.e. the gaps between successive observations on the circumference of the circle. These sample arc-lengths are analogous to sample spacings, which are the gaps between successive observations on the real line. Such a Gini mean difference test is analogous to Rao's spacings test, which has been used to test the uniformity of circular data. We obtain both the exact and asymptotic distributions of the Gini mean difference arc-lengths test, under the null hypothesis of circular uniformity. We also provide a table of upper percentile values of the exact distribution for small to moderate sample sizes. Some examples of circular data analysis are also considered. It is also seen that the Gini mean difference arc-lengths tests is more asymptotically efficient than Rao's test in the sense of Pitman asymptotic relative efficiency.
Category: Statistics

[23] viXra:1007.0016 [pdf] submitted on 13 Mar 2010

Studies in Statistical Inference, Sampling Techniques and Demography

Authors: Rajesh Singh, Jayant Singh, Florentin Smarandache
Comments: 64 pages

This volume is a collection of five papers. Two chapters deal with problems in statistical inference, two with inferences in finite population, and one deals with demographic problem. The ideas included here will be useful for researchers doing works in these fields.
Category: Statistics

[22] viXra:1006.0046 [pdf] submitted on 18 Jun 2010

U-Statistics Based on Spacings

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 23 pages.

In this paper, we investigate the asymptotic theory for U-statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U-statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit this idea to derive the relevant asymptotic theory both under the null hypothesis and under a sequence of close alternatives. The generalized Gini mean difference of the sample spacings is a prime example of a U-statistic of this type. We show that such a Gini spacings test is analogous to Rao's spacings test. We find the asymptotically locally most powerful test in this class, and it has the same efficacy as the Greenwood statistic.
Category: Statistics

[21] viXra:1005.0068 [pdf] submitted on 11 Mar 2010

Randomness and Optimal Estimation in Data Sampling

Authors: M. Khoshnevisan, S. Saxena, H. P. Singh, S. Singh, Florentin Smarandache
Comments: 63 pages.

The purpose of this book is to postulate some theories and test them numerically. Estimation is often a difficult task and it has wide application in social sciences and financial market. In order to obtain the optimum efficiency for some classes of estimators, we have devoted this book into three specialized sections.
Category: Statistics

[20] viXra:1005.0048 [pdf] submitted on 11 Mar 2010

Estimation of Mean in Presence of Non Response Using Exponential Estimator

Authors: Rajesh Singh, Mukesh Kumar, Manoj K. Chaudhary, Florentin Smarandache
Comments: 11 pages

This paper considers the problem of estimating the population mean using information on auxiliary variable in presence of non response. Exponential ratio and exponential product type estimators have been suggested and their properties are studied. An empirical study is carried out to support the theoretical results.
Category: Statistics

[19] viXra:1005.0020 [pdf] submitted on 8 May 2010

Confidence Intervals for the Pythagorean Formula in Baseball

Authors: David D. Tung
Comments: 27 Pages.

In this paper, we will investigate the problem of obtaining confidence intervals for a baseball team's Pythagorean expectation, i.e. their expected winning percentage and expected games won. We study this problem from two different perspectives. First, in the framework of regression models, we obtain confidence intervals for prediction, i.e. more formally, prediction intervals for a new observation, on the basis of historical binomial data for Major League Baseball teams from the 1901 through 2009 seasons, and apply this to the 2009 MLB regular season. We also obtain a Scheffé-type simultaneous prediction band and use it to tabulate predicted winning percentages and their prediction intervals, corresponding to a range of values for log(RS=RA). Second, parametric bootstrap simulation is introduced as a data-driven, computer-intensive approach to numerically computing confidence intervals for a team's expected winning percentage. Under the assumption that runs scored per game and runs allowed per game are random variables following independent Weibull distributions, we numerically calculate confidence intervals for the Pythagorean expectation via parametric bootstrap simulation on the basis of each team's runs scored per game and runs allowed per game from the 2009 MLB regular season. The interval estimates, from either framework, allow us to infer with better certainty as to which teams are performing above or below expectations. It is seen that the bootstrap confidence intervals appear to be better at detecting which teams are performing above or below expectations than the prediction intervals obtained in the regression framework.
Category: Statistics

[18] viXra:1005.0003 [pdf] submitted on 10 Mar 2010

N-Algebraic Structures and S-N-Algebraic Structures

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 209 pages

In this book, for the first time we introduce the notions of Ngroups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. We expect the reader to be well versed in group theory and have at least basic knowledge about Smarandache groupoids, Smarandache loops, Smarandache semigroups and bialgebraic structures and Smarandache bialgebraic structures.
Category: Statistics

[17] viXra:1004.0076 [pdf] submitted on 8 Mar 2010

Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 8 pages

In this paper exponential ratio and exponential product type estimators using two auxiliary variables are proposed for estimating unknown population variance Sy2. Problem is extended to the case of two-phase sampling. Theoretical results are supported by an empirical study.
Category: Statistics

[16] viXra:1004.0064 [pdf] submitted on 8 Mar 2010

Improvement in Estimating Population Mean Using Two Auxiliary Variables in Two-Phase Sampling

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 11 pages

This study proposes improved chain-ratio type estimator for estimating population mean using some known values of population parameter(s) of the second auxiliary character. The proposed estimators have been compared with two-phase ratio estimator and some other chain type estimators. The performances of the proposed estimators have been supposed with a numerical illustration.
Category: Statistics

[15] viXra:1004.0063 [pdf] submitted on 8 Mar 2010

Optimum Statistical Test Procedure

Authors: Rajesh Singh, Jayant Singh, Florentin Smarandache
Comments: 16 pages

Optimum Statistical Test Procedure
Category: Statistics

[14] viXra:1004.0062 [pdf] submitted on 8 Mar 2010

Ratio-Product Type Exponential Estimator for Estimating Finite Population Mean Using Information on Auxiliary Attribute

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 15 pages

In practice, the information regarding the population proportion possessing certain attribute is easily available see Jhajj et.al. (2006). For estimating the population mean Y of the study variable y, following Bahl and Tuteja (1991), a ratio-product type exponential estimator has been proposed by using the known information of population proportion possessing an attribute (highly correlated with y) in simple random sampling. The expressions for the bias and the mean-squared error (MSE) of the estimator and its minimum value have been obtained. The proposed estimator has an improvement over mean per unit estimator, ratio and product type exponential estimators as well as Naik and Gupta (1996) estimators. The results have also been extended to the case of two phase sampling. The results obtained have been illustrated numerically by taking some empirical populations considered in the literature.
Category: Statistics

[13] viXra:1004.0061 [pdf] submitted on 8 Mar 2010

Almost Unbiased Exponential Estimator for the Finite Population Mean

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 12 pages

In this paper we have proposed an almost unbiased ratio and product type exponential estimator for the finite population mean Y-bar. It has been shown that Bahl and Tuteja (1991) ratio and product type exponential estimators are particular members of the proposed estimator. Empirical study is carried to demonstrate the superiority of the proposed estimator.
Category: Statistics

[12] viXra:1004.0056 [pdf] submitted on 8 Mar 2010

Almost Unbiased Ratio and Product Type Estimator of Finite Population Variance Using the Knowledge of Kurtosis of an Auxiliary Variable in Sample Surveys

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 11 pages

It is well recognized that the use of auxiliary information in sample survey design results in efficient estimators of population parameters under some realistic conditions. Out of many ratio, product and regression methods of estimation are good examples in this context. Using the knowledge of kurtosis of an auxiliary variable Upadhyaya and Singh (1999) has suggested an estimator for population variance. In this paper, following the approach of Singh and Singh (1993), we have suggested almost unbiased ratio and product-type estimators for population variance.
Category: Statistics

[11] viXra:1004.0054 [pdf] submitted on 8 Mar 2010

Alternatives to Pearson's and Spearman's Correlation Coefficients

Authors: Florentin Smarandache
Comments: 9 pages

This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixture of Pearson's and Spearman's gives a better result.
Category: Statistics

[10] viXra:1003.0183 [pdf] submitted on 6 Mar 2010

A Note on Testing of Hypothesis

Authors: Rajesh Singh, Jayant Singh, Florentin Smarandache
Comments: 5 pages

In this paper problem of testing of hypothesis is discussed when the samples have been drawn from normal distribution. The study of hypothesis testing is also extended to Baye's set up.
Category: Statistics

[9] viXra:1003.0172 [pdf] submitted on 6 Mar 2010

A General Family of Estimators for Estimating Population Mean Using Known Value of Some Population Parameter(s)

Authors: M. Khoshnevisan, Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 11 pages

A general family of estimators for estimating the population mean of the variable under study, which make use of known value of certain population parameter(s), is proposed. Under Simple Random Sampling Without Replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to first order of approximation are derived. Some well known estimators have been shown as particular member of this family. An empirical study is carried out to illustrate the performance of the constructed estimator over others.
Category: Statistics

[8] viXra:1003.0137 [pdf] submitted on 6 Mar 2010

Empirical Study in Finite Correlation Coefficient in Two Phase Estimation

Authors: M. Khoshnevisan, F. Kaymram, Housila P. Singh, Rajesh Singh, Florentin Smarandache
Comments: 10 pages

This paper proposes a class of estimators for population correlation coefficient when information about the population mean and population variance of one of the variables is not avaliable but information about these parameters of another variable (auxiliary) is avaliable, in two phase sampling and analyzes its properties. Optimum estimator in the class is identified with its variance formula. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters.Following Singh (1982) and Srivastava and Jhajj (1983), it has been shown that when these population parameters are replaced by their consistent estimates the resulting class of estimators has the same asymptotic variance as that of optimum estimator. An empirical study is carried out to demonstrate the performance of the constructed estimators.
Category: Statistics

[7] viXra:1003.0136 [pdf] submitted on 6 Mar 2010

Econometric Analysis on Efficiency of Estimator

Authors: M. Khoshnevisan, F. Kaymram, Housila P. Singh, Rajesh Singh, Florentin Smarandache
Comments: 11 pages

This paper investigates the efficiency of an alternative to ratio estimator under the super population model with uncorrelated errors and a gammadistributed auxiliary variable. Comparisons with usual ratio and unbiased estimators are also made.
Category: Statistics

[6] viXra:1003.0130 [pdf] submitted on 6 Mar 2010

A Family of Estimators of Population Mean Using Multiauxiliary Information in Presence of Measurement Errors

Authors: Jack Allen, Housila P. Singh, Florentin Smarandache
Comments: 16 pages

This paper proposes a family of estimators of population mean using information on several auxiliary variables and analyzes its properties in the presence of measurement errors.
Category: Statistics

[5] viXra:1003.0128 [pdf] submitted on 6 Mar 2010

Estimation of Weibull Shape Parameter by Shrinkage Towards an Interval Under Failure Censored Sampling

Authors: Housila P. Singh, Sharad Saxena, Jack Allen, Sarjinder Singh, Florentin Smarandache
Comments: 20 pages

This paper is speculated to propose a class of shrinkage estimators for shape parameter β in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter β is available in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency and absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed interval of the parameter space of β, especially for censored samples with small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties.
Category: Statistics

[4] viXra:1003.0113 [pdf] submitted on 6 Mar 2010

Improvement in Estimating the Population Mean Using Exponential Estimator in Simple Random Sampling

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 6 pages

This study proposes some exponential ratio-type estimators for estimating the population mean of the variable under study ... (see paper for full abstract)
Category: Statistics

[3] viXra:1003.0109 [pdf] submitted on 6 Mar 2010

A General Class of Estimators of Population Median Using Two Auxiliary Variables in Double Sampling

Authors: Jack Allen, Housila P. Singh, Sarjinder Singh, Florentin Smarandache
Comments: 21 pages

In this paper we have suggested two classes of estimators for population median MY of the study character Y using information on two auxiliary characters X and Z in double sampling. It has been shown that the suggested classes of estimators are more efficient than the one suggested by Singh et al (2001). Estimators based on estimated optimum values have been also considered with their properties. The optimum values of the first phase and second phase sample sizes are also obtained for the fixed cost of survey.
Category: Statistics

[2] viXra:1003.0092 [pdf] submitted on 6 Mar 2010

Auxiliary Information and a Priori Values in Construction of Improved Estimators

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 75 pages

This volume is a collection of six papers on the use of auxiliary information and a priori values in construction of improved estimators. The work included here will be of immense application for researchers and students who employ auxiliary information in any form.
Category: Statistics

[1] viXra:1003.0091 [pdf] submitted on 6 Mar 2010

Ratio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 7 pages

Some ratio estimators for estimating the population mean of the variable under study, which make use of information regarding the population proportion possessing certain attribute, are proposed. Under simple random sampling without replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to the first order of approximation are derived. The results obtained have been illustrated numerically by taking some empirical population considered in the literature.
Category: Statistics

Recent Replacements

[6] viXra:1111.0073 [pdf] replaced on 2011-11-25 09:15:23

Kullback-Leibler Simplex

Authors: Popon Kangpenkae
Comments: 12 Pages.

This technical reference presents the functional structure and the algorithmic implementation of KL (Kullback-Leibler) simplex. It details the simplex approximation and fusion. The KL simplex is fundamental, robust, adaptive an informatics agent for computational research in economics, finance, game and mechanism. From this perspective the study provides comprehensive results to facilitate future work in such areas.
Category: Statistics

[5] viXra:1111.0073 [pdf] replaced on 25 Nov 2011

Kullback-Leibler Simplex

Authors: Popon Kangpenkae
Comments: 12 pages

This technical reference presents the functional structure and the algorithmic implementation of KL (Kullback-Leibler) simplex. It details the simplex approximation and fusion. The KL simplex is fundamental, robust, adaptive an informatics agent for computational research in economics, finance, game and mechanism. From this perspective the study provides comprehensive results to facilitate future work in such areas.
Category: Statistics

[4] viXra:1007.0034 [pdf] replaced on 2012-01-11 19:14:18

On the Gini Mean Difference Test for Circular Data

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 14 Pages.

In this paper, we propose a new test of uniformity on the circle based on the Gini mean difference of the sample arc-lengths. These sample arc-lengths, which are the gaps between successive observations on the circumference of the circle, are analogous to sample spacings on the real line. The Gini mean difference, which compares these arc-lengths between themselves, is analogous to Rao's spacings statistic, which has been used to test the uniformity of circular data. We obtain both the exact and asymptotic distributions of the Gini mean difference arc-lengths test, under the null hypothesis of circular uniformity. We also provide a table of upper percentile values of the exact distribution for small to moderate sample sizes. Illustrative examples in circular data analysis are also given. It is shown that a generalized Gini mean difference test has better asymptotic efficiency than the corresponding generalized Rao's test in the sense of Pitman asymptotic relative efficiency.
Category: Statistics

[3] viXra:1007.0034 [pdf] replaced on 16 Aug 2010

On the Gini Mean Difference Arc-Lengths Test for Circular Data

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 14 pages.

In this paper, we propose a new test of uniformity on the circle based on the Gini mean difference of the sample arc-lengths. These sample arc-lengths, which are the gaps between successive observations on the circumference of the circle, are analogous to sample spacings on the real line. The Gini mean difference, which compares these arc-lengths between themselves, is analogous to Rao's spacings statistic, which has been used to test the uniformity of circular data. We obtain both the exact and asymptotic distributions of the Gini mean difference arc-lengths test, under the null hypothesis of circular uniformity. We also provide a table of upper percentile values of the exact distribution for small to moderate sample sizes. Illustrative examples in circular data analysis are also given. It is shown that a generalized Gini mean difference test has better asymptotic efficiency than the corresponding generalized Rao's test in the sense of Pitman asymptotic relative efficiency.
Category: Statistics

[2] viXra:1006.0046 [pdf] replaced on 2012-01-11 19:16:15

U-Statistics Based on Spacings

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 23 Pages.

In this paper, we investigate the asymptotic theory for U-statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U-statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit this idea to derive the relevant asymptotic theory both under the null hypothesis and under a sequence of close alternatives. The generalized Gini mean difference of the sample spacings is a prime example of a U-statistic of this type. We show that such a Gini spacings test is analogous to Rao's spacings test. We find the asymptotically locally most powerful test in this class, and it has the same efficacy as the Greenwood statistic.
Category: Statistics

[1] viXra:1006.0046 [pdf] replaced on 16 Aug 2010

U-Statistics Based on Spacings

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 23 pages.

In this paper, we investigate the asymptotic theory for U-statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U-statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit this idea to derive the relevant asymptotic theory both under the null hypothesis and under a sequence of close alternatives. The generalized Gini mean difference of the sample spacings is a prime example of a U-statistic of this type. We show that such a Gini spacings test is analogous to Rao's spacings test. We find the asymptotically locally most powerful test in this class, and it has the same efficacy as the Greenwood statistic.
Category: Statistics