[4] **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

[3] **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

[2] **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

[1] **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