Statistics

The diffusion equation is solved in two dimensions to obtain the concentration by using separation of variables under the variation of eddy diffusivity which depend on the vertical height in unstable case. Comparing between the predicted and the observed concentrations data of Sulfur hexafluoride (SF6) taken on the Copenhagen in Denmark is done. The statistical method is used to know the best model. One finds that there is agreement between the present, Laplace and separation predicted normalized crosswind integrated concentrations with the observed normalized crosswind integrated concentrations than the predicted Gaussian model. One gets that the four models are inside a factor of two with observed data. Regarding to NMSE and FB, the present, Laplace and separation predicted models are well with observed data than the Gaussian model. The correlation of present, Laplace and separation predicated model equals (0.52, 0.64 and 0.60 respectively) and Gaussian model equals (0.80).

The present study is an attempt to find out appropriate ARIMA model by using Box-Jenkins methodology to forecast the export/import of wood based panel in India on time series data for a period of 16 years from 1996-97 to 2011-12. Test criterion like lowest Bayesian Information Criterion (BIC), R2 value and lowest of mean absolute percentage error (MAPE) are applied to predict the accuracy of the model. This study found ARIMA (0,1,0) with R2: 0.83 for the export and ARIMA (0,1,1) with R2: 0.87 for the import to forecast of export/import of wood based panel. The estimated export and import of wood based panels in the year 2020 would be increased by 170% and 127% in respect to 2012.

This paper presents Maximum likelihood (M L) estimation approach to derive reliability measures of a two component identical system in the presence of Common Cause Shock failures (CCS) as well as human errors. The M L estimates of system reliability measures like frequency of failures were derived for both series and parallel systems. We also developed the confidence interval in the present study. The approach used is empirical one with Monte Carlo simulation.

In order to solve the reliability assessment of repairable systems, this article, based on two-component system, provides the maximum likelihood estimation. The system can be restored through proper repairing even from Common Cause Shock (CCS) failure. We derived M L estimates of availability for series and parallel systems. The approach used is empirical one with Monte Carlo simulation.

We propose a systematic methodology in any experimental design using orthogonal approach technique, which maximizes the coverage by comparatively lesser number of test cases. In such technique we have to balance between the specified time and quality. In this paper we adopt multiple strategy of OATS (Orthogonal array testing Strategies) in diabetic people to asses and compare the practice to optimize the testing efforts and achieve the right balance between diet and medication in urban and rural areas. Here we introduce three case studies of this orthogonal approach to reduce the number of test cases under the given software and hence improve the efficiency of the testing.

This paper studied and fit a Multivariate linear regression model to the relationship between the response variables; Weight and Bulk density on one hand, and the predictor variables; Temperature, Moisture content before extrusion and Moisture content after extrusion on the other hand, of Cheese puffs product, manufactured by Zubix Company Limited, Anambra, Nigeria. A sample size of three hundred (300) cheese puffs packs were collected from a population of two-thousand, seventy-eight batches between August 2013 to June 2014, examined and used for analysis. A temperature of 186.67?C was discovered to be significantly related to the response variable.

The modern critical analysis of Bose–Einstein and Fermi–Dirac statistics is proposed. Methodological basis of analysis is the unity of formal logic and rational dialectics. It is shown that Bose–Einstein and Fermi–Dirac statistics – as consequence of Bose's erroneous method – contain logical errors. The main error is that Bose–Einstein and Fermi–Dirac distribution functions contain chemical potential. It is proved that chemical potential is identically equal to zero because the concept of chemical potential is contrary to the concept of temperature. There exist the only one correct statistics in statistical physics: Gibbs statistics.

The overriding problem with analyzing unbalanced data which leads to heteroscedasity models is that many methods are available and deciding between them can be a matter of some difficulty. Heteroscedasticity is a problem because ordinary least squares (OLS) in regression assumes that all residuals are drawn from a population that has a constant variance (homoscedasticity). When conditional heteroscedasticity is present, the practice of reweighting the data has long been abandoned in favor of estimating model parameters by ordinary OLS, in conjunction with using heteroscedasticity consistent standard errors. However, we argue for reintroducing the practice of reweighting the data, since doing so can lead to large efficiency gains of the resulting weighted least squares WLS estimator over OLS even when the model for reweighting the data is misspecified. The idea is that, the estimator can also be accompanied by the help of type of proportionality condition on cell sample size using harmonic mean. Special emphasis is given to nested model and on the unbalancedness in the data due to heterogeneity in the environmental conditions of experiments. Estimators of the parameters for this model are found to be independent of the weights under this condition.

The increased reach of health programs in India, during the past few decades, has significantly contributed to declining in postnatal mortality including the infant, child & other mortality. However, reduction in neonatal mortality remained negligible. About 70% neonatal deaths take place within a week after birth. The prime objective of this study is to explore the death clustering of the neonates and its determinants in India. 3rd round of National Family Health Survey (NFHS-3), India, 2005-06 data was used for this study. Bivariate analysis followed by multivariate analysis (Binary logistic regression) was performed to identify the determinants of neonatal mortality. Moran’s I & Univariate LISA cluster map was used to explore the spatial clusters of neonatal deaths in India. Univariate Moran’s I (Moran’s I=0.215) was significant i.e. spatial dependence exists for neonatal deaths in Indian states. The Univariate LISA cluster map explored significant hotspots of neonatal deaths which were Bihar, Chhattisgarh, Jharkhand, MP, Odisha, Rajasthan, UP and WB. The estimated odds of neonatal death was 2.75 times higher (OR=2.75; 95% CI: 2.21-3.43) among smaller size neonates than the average & larger size neonates. The odds of neonatal death was found 2.39 times, 2.73 times & 1.84 times higher among those mothers who had an illiterate, primary & secondary level of education as compared to mothers who had higher education. The risk of neonatal death among 1st (OR=1.43) and more than 4th (OR=1.35) order births was positively higher than 2nd to 3rd order births. Based on the findings, the study proposes various approaches to address the increasing contribution of neonatal deaths in India. The findings suggest that raising mother education & providing a healthy diet to pregnant women, can bring a quick substantial reduction of neonatal mortality and the target fixed can be achieved. So, it is necessary to encourage & support women for higher education. This study proposes to provide the combination of the continuum care for maternal, neonatal, and child health by integrating a family-community based service delivery approach with the existing health care system especially to the death clusters in India.

The primary aim of the present work is to prepare a generalized exponential type estimators for estimation of the population mean under simple random sampling and qualitative auxiliary information. The expressions for MSE have been obtained. A comparison between proposed estimators with some existing estimators is done theoretically as well as numerically.