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Any replacements are listed further down
[35] viXra:1112.0092 [pdf] submitted on 2011-12-31 06:41:31
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
[6] viXra:1111.0073 [pdf] replaced on 2011-11-25 09:15:23
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
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
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
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
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
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