The purpose of writing this book is to suggest some improved estimators
using auxiliary information in sampling schemes like simple random sampling,
systematic sampling and stratified random sampling.
This volume is a collection of five papers, written by nine co-authors
(listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr.
Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil
Prajapati, Hemant Verma, and Viplav Kr. Singh.
In first paper dual to ratio-cum-product estimator is suggested and its
properties are studied. In second paper an exponential ratio-product type
estimator in stratified random sampling is proposed and its properties are
studied under second order approximation. In third paper some estimators are
proposed in two-phase sampling and their properties are studied in the
presence of non-response.
In fourth chapter a family of median based estimator is proposed in
simple random sampling. In fifth paper some difference type estimators are
suggested in simple random sampling and stratified random sampling and their
properties are studied in presence of measurement error.
Authors: Nigel B. Cook
Comments: 1 Page.
The occurrence of pi in formulae apparently unrelated to geometry was used by Eugene Wigner in his 1960 paper The unreasonable effectiveness of mathematics in the natural sciences. Wigner's example is the Gaussian/normal distribution law, which is an example of obfuscation. Laplace (1782), Gauss (1809), Maxwell (1860) and Fisher (1915) wrote the normal exponential distribution with the square root of pi in the normalization outside the integral. But Stigler in 1982 rewrote the equation with pi in the exponent, making the formula look less mysterious because the exponent is then the area of a circle (in other words, Poisson's exponential distribution, adapted to circular areas, with areas expressed in dimensionless form); if you think of the use of the normal distribution to model CEP error probabilities for missiles landing around a target point. (Please see paper for equations.)
Authors: Yuri Heymann
Comments: 11 Pages.
This paper aims to offer a testing framework for the structural properties of the Brownian motion of the underlying stochastic process of a time series. In particular, the test can be applied to financial time-series data and discriminate among the lognormal random walk used in the Black-Scholes-Merton model, the Gaussian random walk used in the Ornstein-Uhlenbeck stochastic process, and the square-root random walk used in the Cox, Ingersoll and Ross process. Alpha-level hypothesis testing is provided. This testing framework is helpful for selecting the best stochastic processes for pricing contingent claims and risk management.