[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